White, Case, Pratt Principles of Engineering Economic Analysis, 6th Edition solution manual by TBtutors

Type:

Solution Manual

Resource:

Principles of Engineering Economic Analysis

Edition:

6th Edition

Author(s):

John A. White Kenneth E. Case David B. Pratt

A 1 PROBLEM 1.1 2 3 4 5 6 7 8 9

WYLIE IS OFFERED THIS AMOUNT NOW=

$5,000.00

WYLIE IS WILLING TO TAKE THIS AMOUNT IN A YEAR=

$5,700.00

THE INCREASE REQ'D BY WYLIE OVER ONE YEAR=

$700.00 =$5,700.00-$5,000.00

THEREFORE WYLIE'S TVOM =

14.00% =$700.00/$5,000.00

A 1 PROBLEM 1.2 2 3 4 5 6 7 8 9 10 11 12 13 14 15 a 16 17 b 18 19 20

RT LOANS=

$20,000.00

RT'S TVOM=

8.00%

RT INTEREST REQ'D=

$1,600.00

CYNTHIA BORROWS=

$20,000.00

CYNTHIA'S TVOM= CYNTHIA'S EARNINGS=

12.00% $2,400.00

YES, THEY SHOULD BE ABLE TO NEGOTIATE THE LOAN RT REQUIRES $1,600 OR MORE IN INTEREST CYNTHIA IS WILLING TO PAY $2400 OR LESS IN INTEREST THE ACCEPTABLE RANGE IS FROM $1,600 TO $2,400

A 1 PROBLEM 1.3 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

a b

RT LOANS= $20,000.00 RT'S TVOM= 12.00% RT INTEREST REQ'D= $2,400.00 MINIMUM INTEREST REQUIRED BY RT CYNTHIA BORROWS= $20,000.00 CYNTHIA'S TVOM= 8.00% CYNTHIA'S EARNINGS= $1,600.00 WILLING TO PAY= $2,000.00 MAXIMUM INTEREST CYNTHIA WILLING TO PAY NO, THEY SHOULD NOT BE ABLE TO NEGOTIATE THE LOAN UNLESS ONE OR BOTH CHANGE THEIR MIND RT REQUIRES $2,400 OR MORE IN INTEREST CYNTHIA CAN EARN $1,600 ON HER MONEY; HOWEVER, CYNTHIA IS WILLING TO PAY $2,000 IN INTEREST CYNTHIA'S MONEY MUST BE INVESTED AND SHE NEEDS TO BORROW MONEY NOW, EVEN IF SHE HAS TO PAY $2,000 IN INTEREST. THERE IS STILL NO ACCEPTABLE RANGE. RT REQUIRES $2,400 OR MORE IN INTEREST; CYNTHIA WILL PAY $2,000 OR LESS. THEY ARE $400 OFF

A B 1 PROBLEM 1.4 2 3 LOAN AMOUNT= 4 5 YOUR TVOM= 6 7 FRIEND'S TVOM= 8

9 10 11 12

$3,000.00 15.00% OR

$450.00 INTEREST

20.00% OR

$600.00 INTEREST

YOU ARE WILLING TO MAKE THE LOAN TO YOUR FRIEND FOR $450.00 INTEREST OR MORE. YOUR FRIEND IS WILLING TO ACCEPT THE LOAN FOR $600 INTEREST OR LESS. SO, ANY INTEREST NEGOTIATION WITH YOU AS THE LENDER THAT IS ACCEPTABLE TO BOTH PARTIES IS BETWEEN $450 AND $600. YOUR FRIEND IS WILLING TO MAKE THE LOAN TO YOU FOR $600 INTEREST OR MORE. YOU ARE WILLING TO ACCEPT THE LOAN FOR $450 INTEREST OR LESS. SO, THE ACCEPTABILITY GAP BETWEEN YOU AND YOUR FRIEND IS $150.

1 2 3 4 5 6 7 8

A PROBLEM 1.5

STAGE 1 2 3 4

INVESTMENT STATION ANTENNA AMPLIFIER LIGHTNING PROTECTION CONTROL CONSOLE

9 5 10 11

12 13 14

COSTS IN REVS IN NET CUM CUM CUM TODAY'S $ TODAY'S $ REV-COST COSTS REVS REV-COST $180,000 $270,000 $90,000 $180,000 $270,000 $90,000 $30,000 $50,000 $20,000 $210,000 $320,000 $110,000 $40,000 $30,000 -$10,000 $250,000 $350,000 $100,000 $30,000

$60,000

$30,000 $280,000 $410,000

$130,000

$15,000

$5,000

-$10,000 $295,000 $415,000

$120,000

PURCHASE THE FIRST FOUR STAGES. NOTE THAT THIS GIVES THE HIGHEST ACCUMULATED TOTAL NET REVENUE-COST. IN TODAY'S $. NOTE THAT THE AMPLIFIER DOES NOT PAY OUT, BUT IT IS NECESSARY FOR THE LIGHTNING PROTECTION THAT PAYS OUT NICELY

2. MAKE INVESTMENTS THAT ARE ECONOMICALLY JUSTIFIED 3. CHOOSE THE MUTUALLY EXCLUSIVE INVESTMENT ALTERNATIVE THAT MAXIMIZES ECONOMIC WORTH 5. MARGINAL REVENUE MUST EXCEED MARGINAL COST 6. MONEY SHOULD CONTINUE TO BE INVESTED AS LONG AS EACH ADDITIONAL INCREMENT OF INVESTMENT YIELDS A RETURN THAT IS GREATER THAN THE INVESTOR'S TVOM

1. IDENTIFY THE INVESTMENT ALTERNATIVES 5. COMPARE THE ALTERNATIVES 7. SELECT THE PREFERRED ALTERNATIVE

15 16

18 19 20 21

A B C D E 1 PROBLEM 1.6 2 3 ORIGINAL WSI BID= $5,500.00 4 5 BARB & FRED EXPENSES= $1,900.00 6 $1,100.00 MATERIALS - NO RETURN 7 $400.00 TRENCHER AT $80 FOR 5 DAYS 8 $400.00 JACKHAMMER AT $80 FOR 5 DAYS 9 10 REVISED WSI BID= $4,500.00 11 $5,500.00 ORIGINAL 12 -$500.00 MATERIALS 13 -$500.00 TRENCHING 14 15 a $1,900.00 BARBARA AND FRED HAVE ALREADY SPENT 16 17 b $6,400.00 TOTAL SPENT AFTER WSI 18 19 c $6,000.00 SS CHARGE GO WITH WSI, NOT SS. COMPARING SS AT $6,000 AND WSI AT $6,400 TAKES INTO ACCOUNT SUNK COSTS 20 21 SUNK COSTS SHOULD NOT BE CONSIDERED. 22 23 $4,500 FUTURE SPENDING WITH WSI 24 25 $6,000 FUTURE SPENDING WITH SS 26 27 GO WITH WSI, NOT SS. 28 29 d 2. MAKE INVESTMENTS THAT ARE ECONOMICALLY JUSTIFIED 10. PAST COSTS ARE IRRELEVANT IN ENGINEERING ECONOMIC ANALYSES, UNLESS THEY IMPACT FUTURE COSTS 30 31 32 e 1. IDENTIFY THE INVESTMENT ALTERNATIVES 33 4. ESTIMATE THE CASH FLOWS 34 5. COMPARE THE ALTERNATIVES 35 7. SELECT THE PREFERRED ALTERNATIVE

F 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

A B 1 PROBLEM 1.7 2 3 a EXAMPLES OF NON-MONETARY FACTORS INCLUDE: 4 QUALITY 5 SAFETY 6 ENVIRONMENTAL IMPACT 7 COMMUNITY ATTITUDES 8 LABOR-MANAGEMENT RELATIONSHIPS 9 SYSTEM RELIABILITY 10 SYSTEM AVAILABILITY 11 SYSTEM MAINTAINABILITY 12 SYSTEM OPERABILITY 13 SYSTEM FLEXIBILITY 14 IMPACT ON PERSONNEL LEVELS 15 TRAINING REQUIREMENTS 16 COMPARISON WITH COMPETITORS 17 IMPACT ON DIFFERENT UNITS WITHIN THE ORGANIZATION 18 BRINGING ABOUT CHANGE 19 EGO 20 CUSTOMER PREFERENCES 21 DEPENDING UPON WHAT TYPES OF ALTERNATIVES ARE BEING CONSIDERED, THIS LIST 22 COULD BE ALMOST LIMITLESS. 23 24 b NONE 25 26 c 5. COMPARE THE ALTERNATIVES 27 6. PERFORM SUPPLEMENTARY ANALYSES 28 7. SELECT THE PREFERRED ALTERNATIVE

A B C D E F G H 1 PROBLEM 1.8 2 3 ACCEPT PROPOSAL: 1 4 REJECT PROPOSAL: 0 5 6 a ALT PROP PROP PROP PROP WHY NOT FEASIBLE 7 A B C D 8 9 1 0 0 0 0 10 2 0 0 0 1 11 3 0 0 1 0 12 4 0 0 1 1 13 5 0 1 0 0 B CONTINGENT ON C OR D 14 6 0 1 0 1 15 7 0 1 1 0 16 8 0 1 1 1 17 9 1 0 0 0 A CONTINGENT ON D 18 10 1 0 0 1 19 11 1 0 1 0 NOT BOTH A AND C A CONTINGENT ON D 20 12 1 0 1 1 NOT BOTH A AND C 21 13 1 1 0 0 B CONTINGENT ON C OR D A CONTINGENT ON D 22 14 1 1 0 1 23 15 1 1 1 0 NOT BOTH A AND C A CONTINGENT ON D 24 16 1 1 1 1 NOT BOTH A AND C 25 26 b NONE 27 28 c 1. IDENTIFY THE INVESTMENT ALTERNATIVES

A B C D E F G H 1 PROBLEM 1.9 2 3 ACCEPT PROPOSAL: 1 REJECT PROPOSAL: 0 4 5 a ALT PROP PROP PROP PROP PROP WHY NOT FEASIBLE 6 V W X Y Z 7 1 0 0 0 0 0 AT LEAST 2 AND NO MORE THAN 4 2 0 0 0 0 1 AT LEAST 2 AND NO MORE THAN 4; Z 8 CONTINGENT ON X OR Y 9 3 0 0 0 1 0 AT LEAST 2 AND NO MORE THAN 4 10 4 0 0 0 1 1 11 5 0 0 1 0 0 AT LEAST 2 AND NO MORE THAN 4 12 6 0 0 1 0 1 13 7 0 0 1 1 0 X AND Y MUTUALLY EXCLUSIVE 14 8 0 0 1 1 1 X AND Y MUTUALLY EXCLUSIVE 15 9 0 1 0 0 0 AT LEAST 2 AND NO MORE THAN 4 16 10 0 1 0 0 1 Z CONTINGENT ON X OR Y 17 11 0 1 0 1 0 18 12 0 1 0 1 1 19 13 0 1 1 0 0 20 14 0 1 1 0 1 21 15 0 1 1 1 0 X AND Y MUTUALLY EXCLUSIVE 22 16 0 1 1 1 1 X AND Y MUTUALLY EXCLUSIVE 23 17 1 0 0 0 0 AT LEAST 2 AND NO MORE THAN 4 24 18 1 0 0 0 1 Z CONTINGENT ON X OR Y 25 19 1 0 0 1 0 NOT V IF W, X, Y 26 20 1 0 0 1 1 NOT V IF W, X, Y 27 21 1 0 1 0 0 NOT V IF W, X, Y 28 22 1 0 1 0 1 NOT V IF W, X, Y X AND Y MUTUALLY EXCLUSIVE; NOT V 23 1 0 1 1 0 IF W, X, Y 29 X AND Y MUTUALLY EXCLUSIVE; NOT V 24 1 0 1 1 1 IF W, X, Y 30 31 25 1 1 0 0 0 NOT V IF W, X, Y 32 26 1 1 0 0 1 Z CONTINGENT ON X OR Y 33 27 1 1 0 1 0 NOT V IF W, X, Y 34 28 1 1 0 1 1 NOT V IF W, X, Y 35 29 1 1 1 0 0 NOT V IF W, X, Y 36 30 1 1 1 0 1 NOT V IF W, X, Y X AND Y MUTUALLY EXCLUSIVE; NOT V 31 1 1 1 1 0 IF W, X, Y 37 32 1 1 1 1 1 AT LEAST 2 AND NO MORE THAN 4; X AND Y MUTUALLY EXCLUSIVE; NOT V IF 38 W, X, Y 39 40 b NONE 41 42 c 1. IDENTIFY THE INVESTMENT ALTERNATIVES

A B C D E F 1 PROBLEM 1.10 2 3 ACCEPT PROPOSAL: 1 REJECT PROPOSAL: 0 4 5 ALTERNATIVE PROPOSAL PROPOSAL PROPOSAL WHY NOT FEASIBLE 6 P Q R 7 8 1 0 0 0 EXACTLY 1 OR 2 CHOSEN 9 2 0 0 1 R CONTINGENT ON P 10 3 0 1 0 11 4 0 1 1 R CONTINGENT ON P 12 5 1 0 0 13 6 1 0 1 14 7 1 1 0 P AND Q MUTUALLY EXCLUSIVE EXACTLY 1 OR 2 CHOSEN; P AND 8 1 1 1 Q MUTUALLY EXCLUSIVE 15

A B C D E F G H 1 PROBLEM 1.11 2 3 NOTE TO INSTRUCTOR 4 THIS IS AN INTERESTING PROBLEM, ESPECIALLY WHEN DISCUSSED WITH 5 ITS COMPANION PROBLEM 1.12 6 7 WHAT YOU SHOULD KNOW ABOUT THIS PROBLEM IS: 8 9 THERE IS NO SINGLE CORRECT ANSWER 10 THE EXPECTED VALUE (PROBABILITY-WEIGHTED RETURNS LESS 11 PROBABILITY-WEIGHTED FAILURES) IS THE SAME FOR EACH: $10.00. 12 13 ECONOMICALLY SPEAKING, THE THREE ARE EQUIVALENT 14 ONE WHO SELECTS ALTERNATIVE A IS RISK AVERSE (OR QUITE 15 CONSERVATIVE) - MANY WILL GAMBLE $100 ON B OR C 16 THE STUDENTS SHOULD NOT BE EXPECTED TO DO A PROBABILISTIC 17 ANALYSIS - THEY WILL SEE HOW TO DO THAT IN CHAPTER 13 18 THE STUDENTS SHOULD BE EXPECTED TO DO A "GUT" ANALYSIS - HOW 19 WOULD THEY ACTUALLY DECIDE HERE? 20 21 RETURNED RETURNED 22 YOU CHANCE OF TO YOU IF CHANCE OF TO YOU IF EXPECTED 23 ALTERNATIVE INVEST SUCCESS SUCCESS FAILURE FAILURE VALUE 24 A $100.00 95% $110.79 5% $95.00 $10.00 25 B $100.00 60% $150.00 40% $50.00 $10.00 26 C $100.00 20% $510.00 80% $10.00 $10.00 27 28 a I WOULD SELECT ALTERNATIVE A IF PLAYING THIS ONLY ONCE. 29 30 b I STILL DON'T LIKE LOSING $50 OR $90. 31 32 c MAY WISH TO MAKE A CASE FOR 2, 3, 4, 5. NUMBER 9 IS FOR SURE. 33 34 2. MAKE INVESTMENTS THAT ARE ECONOMICALLY JUSTIFIED 3. CHOOSE THE MUTUALLY EXCLUSIVE INVESTMENT ALTERNATIVE THAT 35 MAXIMIZES ECONOMIC WORTH 4. TWO INVESTMENT ALTERNATIVES ARE EQUIVALENT IF THEY HAVE THE 36 SAME ECONOMIC WORTH 37 5. MARGINAL REVENUE MUST EXCEED MARGINAL COST 38 9. RISKS AND RETURNS TEND TO BE POSITIVELY CORRELATED 39 d MAY WANT TO MAKE A CASE FOR 6, WITH THE EV ANALYSIS - ALTHOUGH 40 THAT SHOULD NOT BE EXPECTED 41 42 1. IDENTIFY THE INVESTMENT ALTERNATIVES 43 4. ESTIMATE THE CASH FLOWS 44 5. COMPARE THE ALTERNATIVES 45 6. PERFORM SUPPLEMENTARY ANALYSES 46 7. SELECT THE PREFERRED ALTERNATIVE

A B C D 1 PROBLEM 1.12 2 3 NOTE TO INSTRUCTOR 4

THERE IS NO SINGLE CORRECT ANSWER THE EXPECTED VALUE (PROBABILITY-WEIGHTED RETURNS LESS PROBABILITY-WEIGHTED FAILURES) IS THE SAME FOR EACH: $10,000. ECONOMICALLY SPEAKING, THE THREE ARE EQUIVALENT ONE WHO SELECTS ALTERNATIVE C IS A RISK SEEKER (OR QUITE RISK PRONE) - NOT MANY WILL GAMBLE ON B OR C

15 16

THE STUDENTS SHOULD NOT BE EXPECTED TO DO A PROBABILISTIC ANALYSIS - THEY WILL SEE THAT IN CHAPTER 13

17 18

THE STUDENTS SHOULD BE EXPECTED TO DO A "GUT" ANALYSIS HOW WOULD THEY ACTUALLY DECIDE HERE? RETURNED RETURNED YOU CHANCE OF TO YOU IF CHANCE OF TO YOU IF EXPECTED ALT INVEST SUCCESS SUCCESS FAILURE FAILURE VALUE A $100,000.00 95% $110,789.47 5% $95,000.00 $10,000.00 B $100,000.00 60% $150,000.00 40% $50,000.00 $10,000.00 C $100,000.00 20% $510,000.01 80% $10,000.00 $10,000.00 a

I WOULD SELECT A

IT HAS A 95% CHANCE OF POCKETING A QUICK PROFIT OF $10,789.47 WITH ONLY $5,000 DOWNSIDE

MAY WISH TO MAKE A CASE FOR 2, 3, 4, 5. NUMBER 9 IS FOR SURE. 2. MAKE INVESTMENTS THAT ARE ECONOMICALLY JUSTIFIED 3. CHOOSE THE MUTUALLY EXCLUSIVE INVESTMENT ALTERNATIVE THAT MAXIMIZES ECONOMIC WORTH 4. TWO INVESTMENT ALTERNATIVES ARE EQUIVALENT IF THEY HAVE THE SAME ECONOMIC WORTH 5. MARGINAL REVENUE MUST EXCEED MARGINAL COST 9. RISKS AND RETURNS TEND TO BE POSITIVELY CORRELATED

35 36 37 38 39 40 41 42 43 44 45 46

WHAT YOU SHOULD KNOW ABOUT THIS PROBLEM IS:

11 12 13 14

30 31 32 33 34

THIS IS AN INTERESTING PROBLEM, ESPECIALLY WHEN DISCUSSED WITH ITS COMPANION PROBLEM 1.11.

5 6 7 8 9 10

19 20 21 22 23 24 25 26 27 28 29

MAY WANT TO MAKE A CASE FOR 6, WITH THE EV ANALYSIS ALTHOUGH THAT SHOULD NOT BE EXPECTED 1. IDENTIFY THE INVESTMENT ALTERNATIVES 4. ESTIMATE THE CASH FLOWS 5. COMPARE THE ALTERNATIVES 6. PERFORM SUPPLEMENTARY ANALYSES 7. SELECT THE PREFERRED ALTERNATIVE

A B 1 PROBLEM 1.13 2 AUTOFOUNDRY SHOULD DO NOTHING AT ALL! THEIR ANALYSIS IS INCORRECT, a EVEN IF ALL DATA WERE RIGHT. 3 4 THE MAJOR FLAW IS THAT THE TIME HORIZON IN ONE CASE IS 5 YEARS AND 9 IN THE OTHER. 5 6 7 2. MAKE INVESTMENTS THAT ARE ECONOMICALLY JUSTIFIED 8 b 3. CHOOSE THE MUTUALLY EXCLUSIVE INVESTMENT ALTERNATIVE THAT MAXIMIZES ECONOMIC WORTH 9 4. TWO INVESTMENT ALTERNATIVES ARE EQUIVALENT IF THEY HAVE THE SAME ECONOMIC WORTH 10 5. MARGINAL REVENUE MUST EXCEED MARGINAL COST 11 8. COMPARE INVESTMENT ALTERNATIVES OVER A COMMON PERIOD OF TIME (STRONG) 12 13 1. IDENTIFY THE INVESTMENT ALTERNATIVES 14 c 2. DEFINE THE PLANNING HORIZON (STRONG) 15 4. ESTIMATE THE CASH FLOWS 16 5. COMPARE THE ALTERNATIVES 17 7. SELECT THE PREFERRED ALTERNATIVE 18

A B 1 PROBLEM 1.14 2 USE A 10 YEAR PLANNING HORIZON. THE REASON IS THAT EACH PROJECT IS A ONEa SHOT ALTERNATIVE AND IN ORDER TO CONSIDER EACH, THE PLANNING HORIZON MUST MATCH THAT OF THE LONGEST-LIVED PROJECT OR ALTERNATIVE. 3 4 2. MAKE INVESTMENTS THAT ARE ECONOMICALLY JUSTIFIED 5 b 3. CHOOSE THE MUTUALLY EXCLUSIVE INVESTMENT ALTERNATIVE THAT MAXIMIZES ECONOMIC WORTH 6 8. COMPARE INVESTMENT ALTERNATIVES OVER A COMMON PERIOD OF TIME 7 8 1. IDENTIFY THE INVESTMENT ALTERNATIVES 9 c 2. DEFINE THE PLANNING HORIZON 10 5. COMPARE THE ALTERNATIVES 11 7. SELECT THE PREFERRED ALTERNATIVE 12

A B 1 PROBLEM 1.15 2 VIRTUALLY ANY PLANNING HORIZON COULD BE SELECTED. MOST LIKELY IT WOULD a BE SOME NUMBER OF YEARS FROM THE SHORTEST-LIVED ALTERNATIVE (4 YEARS) TO THE LONGEST-LIVED (10 YEARS), ALTHOUGH THIS IS NOT NECESSARILY SO. THE DECISION MAKER MUST FIRST ASK "OVER WHAT PERIOD OF TIME DO I WANT TO MAKE THE BEST DECISION?" FOR ANY SELECTED PLANNING HORIZON, SAY 6 YEARS FOR EXAMPLE, THE 4 YEAR ALTERNATIVE REQUIRES SPECIFICATION OF WHAT WILL HAPPEN IN YEARS 5 AND 6 (SUCH AS REPAVING) AND THEN WILL REQUIRE ESTIMATION OF A RESIDUAL OR SALVAGE VALUE AT THE END OF YEAR 6. IN THE CASE OF THE RV HOOK UPS, A RESIDUAL OR SALVAGE VALUE WOULD NEED TO BE ESTIMATED AT THE END OF 6 YEARS TO PROPERLY REFLECT THE REMAINING VALUE IN THAT ALTERNATIVE AFTER THE 6 YEAR PLANNING HORIZON. SIMILAR THINKING IS REQUIRED FOR ANY OTHER PLANNING HORIZON SELECTED. 3 4 2. MAKE INVESTMENTS THAT ARE ECONOMICALLY JUSTIFIED 5 b. 3. CHOOSE THE MUTUALLY EXCLUSIVE INVESTMENT ALTERNATIVE THAT MAXIMIZES ECONOMIC WORTH 6 8. COMPARE INVESTMENT ALTERNATIVES OVER A COMMON PERIOD OF TIME 7 8 1. IDENTIFY THE INVESTMENT ALTERNATIVES 9 c. 2. DEFINE THE PLANNING HORIZON 10 5. COMPARE THE ALTERNATIVES 11 7. SELECT THE PREFERRED ALTERNATIVE 12

A B C D E F G H I J K L M 1 PROBLEM 1.16 2 3 a BC CI SW WC 4 FACTOR WT RT SC RT SC RT SC RT SC 5 P 20 9.2 184 10 200 6.7 134 8.2 164 6 Q 30 10 300 7 210 8 240 6 180 7 D 25 9 225 7 175 10 250 7 175 8 R 15 6 90 5 75 7 105 10 150 9 E 10 8 80 9 90 6 60 10 100 10 11 TOTALS 879 750 789 769 12 b QUALITY (Q), DELIVERY (D), AND RELIABILITY (R) ARE ALL BETTER FOR BC THAN FOR CI. THEY OVERCAME THE $85,000 - $79,000 = $6,000 PRICE DIFFERENCE OF CI OVER BC. THEREFORE, THEY MUST 13 BE WORTH AT LEAST $6,000. 14 15 c 2. MAKE INVESTMENTS THAT ARE ECONOMICALLY JUSTIFIED 16 17 d 1. IDENTIFY THE INVESTMENT ALTERNATIVES 18 5. COMPARE THE ALTERNATIVES 19 7. SELECT THE PREFERRED ALTERNATIVE

A B C D E F G H I J K L M 1 PROBLEM 1.17 NOTE! THIS PROBLEM IS SIMILAR TO EXAMPLE 1.8 2 3 a A B C D 4 FACTOR WT RT SC RT SC RT SC RT SC 5 PW 35 6.3 220.5 10 350 7.5 262.5 8.8 308 6 PP 40 9.1 364 7.7 308 10 400 5.8 232 7 RL 25 7.5 187.5 9 225 9 225 10 250 8 9 TOTALS 772 883 887.5 790 10 11 RECOMMEND ALTERNATIVE C BY A SMALL MARGIN OVER B 12 b PAYBACK PERIOD WAS THE DIFFERENCE MAKER IN SELECTING C OVER B, EVEN THOUGH B HAD A HIGHER PRESENT WORTH ($300,000) THAN C ($225,000) FOR A DIFFERENCE OF $75,000. PAYBACK PERIOD FROM 3 TO 1 13 YEARS MUST BE WORTH AT LEAST $75,000 TO THE COMPANY. 14 15 c 2. MAKE INVESTMENTS THAT ARE ECONOMICALLY JUSTIFIED 16 17 d 1. IDENTIFY THE INVESTMENT ALTERNATIVES 18 5. COMPARE THE ALTERNATIVES 19 7. SELECT THE PREFERRED ALTERNATIVE

A B C D E F G 1 PROBLEM 1.18 2 3 COST/GAL G1= $7.50 4 COST/GAL G2= $13.50 5 % BLUE G1= 11.00% 6 % BLUE G2= 22.00% 7 8 DESIRED % BLUE 18.00% 9 X= PROPORTION OF G1 USED IN FINAL MIXTURE 10 1-X= PROPORTION OF G2 USED IN FINAL MIXTURE 11 12 13 a SOLVING FOR X 14 % BLUE FORMULA= 18.00% =11%*X+22%*(1-X) 15 REARRANGING TERMS= 11%*X=4% 16 X= 36.36% =(22.00%-18.00%)/(22.00%-11.00%) 17 1-X= 63.64% =1-36.36% 18 USE 36.36% OF G1 AND 63.64% OF G2 IN THE FINAL PAINT MIXTURE 19 20 b COST EQUATION 21 COST= $11.32 =7.5*36.36%+13.5*(1-36.36%)

A 1 PROBLEM 1.19 2 3 4 5 6 7 8 9 10 11 12 a 13 14 15 16 17 18 b 19 20 21 22 23 24 25 c

ORDER SIZE= OLD MATERIAL COST/UNIT= OLD LABOR COST/UNIT= NEW MATERIAL COST/UNIT= NEW LABOR COST/UNIT= ADDITIONAL TOOLING COST=

500,000 UNITS $0.75 $0.25 $0.52 $0.16 $90,000.00

TOTAL COST = MATERIAL COST + LABOR COST + NON-FACTORY COST CONTINUE OLD METHOD MATERIAL COST= LABOR COST= NON-FACTORY COST= TOTAL COST=

$187,500.00 =(500000/2)*0.75 $62,500.00 =(500000/2)*0.25 $125,000.00 =2*62500 $375,000.00 =187500+62500+125000

SWITCH TO NEW METHOD NEW TOOLING COST= MATERIAL COST= NEW LABOR COST/UNIT= NON-FACTORY COST= TOTAL COST=

$90,000.00 =90000 $130,000.00 =(500000/2)*0.52 $40,000.00 =(500000/2)*0.16 $80,000.00 =2*40000 $340,000.00 =90000+130000+40000+80000

SWITCH TO THE NEW METHOD - LESS COSTLY

A 1 PROBLEM 1.20 2 3 4 5 6 7 8 9 10 11 12 a 13 14 15 16 17 18 19 b 20

COST/GAL A= COST/GAL B= % CRANBERRY A= % CRANBERRY B=

$1.00 $2.50 12.50% 20.00%

DESIRED % CRANBERRY X= 1-X=

15.50% PROPORTION OF CRANBERRY A USED IN FINAL MIXTURE PROPORTION OF CRANBERRY B USED IN FINAL MIXTURE

SOLVING FOR X % CRANBERRY FORMULA 15.50% =12.5%*X+20%*(1-X) REARRANGING TERMS= 7.5%*X=4.5% X= 60.00% =(20.00%-15.50%)/(20.00%-12.50%) 1-X= 40.00% =1-60% USE 60.0% OF A AND 40.0% OF B IN THE FINAL CRANBERRY MIXTURE COST EQUATION COST/GAL=

$1.60 =1*60%+2.5*(1-60%)

A 1 PROBLEM 1.21 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

COST OF RAW MAT'L A PER LB= COST OF RAW MAT'L B PER LB= COST OF RAW MAT'L C PER LB=

$5.18 $1.61 $2.82 ALTERNATIVE 1 ALTERNATIVE 2 ALTERNATIVE 3

COST OF RAW MAT'L A PER UNIT= LBS/UNIT= COST A/UNIT CALCULATIONS ARE= COST A/UNIT=

0.050 =$5.18*0.05 $0.2590

0.070 =$5.18*0.07 $0.3626

0.075 =$5.18*0.075 $0.3885

COST OF RAW MAT'L B PER UNIT= LBS/UNIT= COST B/UNIT CALCULATIONS ARE= COST B/UNIT=

0.190 =$1.61*0.190 $0.3059

0.180 =$1.61*0.180 $0.2898

0.260 =$1.61*0.260 $0.4186

COST OF RAW MAT'L C PER UNIT= LBS/UNIT= COST C/UNIT CALCULATIONS ARE= COST C/UNIT=

0.140 =$2.82*0.140 $0.3948

0.120 =$2.82*0.120 $0.3384

0.170 =$2.82*0.170 $0.4794

TOTAL RAW MAT'L COST/UNIT

$0.9597

$0.9908

$1.2865

OTHER COSTS/UNIT

$0.2400

$0.3600

$0.3400

TOTAL COSTS/UNIT=

$1.1997

$1.3508

$1.6265

PRICE/UNIT=

$1.4300

$1.5800

$1.8800

PROFIT/UNIT

$0.2303

$0.2292

$0.2535

SALES VOLUME=

1,000,000

1,250,000

800,000

TOTAL PROFIT=

$230,300

$286,500

$202,800

SELECT ALTERNATIVE 2 TO MAXIMIZE PROFIT

A 1 PROBLEM 1.22 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 a 18 19 b

LABOR COST PER ACCEPTABLE UNIT

$1.40

COST OF MATERIAL PER UNIT

$5.50

PRODUCTION RATE REJECTION RATE ACCEPTABLE UNITS

100 3.00% 97

125 150 8.00% 20.00% 115 120

LABOR COST AT $1.40/ACCEPTABLE UNIT COST OF MATERIAL AT $5.50 PER UNIT

$135.80 $161.00 $168.00 $550.00 $687.50 $825.00

TOTAL DAILY COSTS COST PER ACCEPTABLE UNIT

$685.80 $848.50 $993.00 $7.07 $7.38 $8.28

WORKERS PREFER 150 UNIT PRODUCTION RATE TO MAX DAILY PAY AT $168.00 PRODUCTION RATE FOR LOWEST UNIT COST PER ACCEPTABLE UNIT IS 100 UNITS

ORDER SIZE COMPARING M1 TO M2: 300+9X=750+3X 6X=450 X=75 COMPARING M1 TO M3 300+9X=500+5X 4X=200 X=50 COMPARING M2 TO M3 750+3X=500+5X 2X=250 X=125

M1 PREFERRED TO M2 AT 75 OR LESS M2 PREFERRED TO M1 AT 75 OR MORE

M1 PREFERRED TO M3 AT 50 OR LESS M3 PREFERRED TO M1 AT 50 OR MORE

M3 PREFERRED TO M2 AT 125 OR LESS M2 PREFERRED TO M3 AT 125 OR MORE

USE M1 FOR X OF 0 TO 50 USE M3 FOR X OF 50 TO 125 USE M2 FOR X OF 125 OR MORE GRAPHICAL REPRESENTATION OF BREAKEVEN POINTS THIS GRAPH WAS DEVELOPED FROM THE TABLE OF COSTS AFTER PART c $2,500.00 $2,000.00 $1,500.00

TOOL M1 TOOL M2

$1,000.00

TOOL M3

$500.00 $0.00

FOR X=75 USE M3 FOR $875

=500+5*75

FOR X=160 USE M2 FOR $1230 IF NOT AVAILABLE, USE M3 FOR $1300

=750+3*160 =500+5*160 PENALTY IS $70 EXTRA OVER M2

IF NEITHER AVAILABLE, USE M1 FOR $1740 =300+9*160 PENALTY IS $510 EXTRA OVER M2 PENALTY IS $440 EXTRA OVER M3

SEE COMPLETE TABLE OF COSTS BELOW

1 13 25 37 49 61 73 85 97 109 121 133 145 157 169 181 193

A 1 PROBLEM 1.23 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 a 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 b 47 48 c 49 50 51 52 53 54 55 56 57

A 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114

FIXED COST= VARIABLE COST/UNIT=

ORDER SIZE 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

C D E MACHINE MACHINE MACHINE TOOL M1 TOOL M2 TOOL M3 $300.00 $750.00 $500.00 $9.00 $3.00 $5.00 MACHINE MACHINE MACHINE TOOL M1 TOOL M2 TOOL M3 $309.00 $753.00 $505.00 $318.00 $756.00 $510.00 $327.00 $759.00 $515.00 $336.00 $762.00 $520.00 $345.00 $765.00 $525.00 $354.00 $768.00 $530.00 $363.00 $771.00 $535.00 $372.00 $774.00 $540.00 $381.00 $777.00 $545.00 $390.00 $780.00 $550.00 $399.00 $783.00 $555.00 $408.00 $786.00 $560.00 $417.00 $789.00 $565.00 $426.00 $792.00 $570.00 $435.00 $795.00 $575.00 $444.00 $798.00 $580.00 $453.00 $801.00 $585.00 $462.00 $804.00 $590.00 $471.00 $807.00 $595.00 $480.00 $810.00 $600.00 $489.00 $813.00 $605.00 $498.00 $816.00 $610.00 $507.00 $819.00 $615.00 $516.00 $822.00 $620.00 $525.00 $825.00 $625.00 $534.00 $828.00 $630.00 $543.00 $831.00 $635.00 $552.00 $834.00 $640.00 $561.00 $837.00 $645.00 $570.00 $840.00 $650.00 $579.00 $843.00 $655.00 $588.00 $846.00 $660.00 $597.00 $849.00 $665.00 $606.00 $852.00 $670.00 $615.00 $855.00 $675.00 $624.00 $858.00 $680.00 $633.00 $861.00 $685.00 $642.00 $864.00 $690.00 $651.00 $867.00 $695.00 $660.00 $870.00 $700.00 $669.00 $873.00 $705.00 $678.00 $876.00 $710.00 $687.00 $879.00 $715.00 $696.00 $882.00 $720.00 $705.00 $885.00 $725.00 $714.00 $888.00 $730.00 $723.00 $891.00 $735.00 $732.00 $894.00 $740.00 $741.00 $897.00 $745.00 $750.00 $900.00 $750.00

A 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171

B 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107

C D E $759.00 $903.00 $755.00 $768.00 $906.00 $760.00 $777.00 $909.00 $765.00 $786.00 $912.00 $770.00 $795.00 $915.00 $775.00 $804.00 $918.00 $780.00 $813.00 $921.00 $785.00 $822.00 $924.00 $790.00 $831.00 $927.00 $795.00 $840.00 $930.00 $800.00 $849.00 $933.00 $805.00 $858.00 $936.00 $810.00 $867.00 $939.00 $815.00 $876.00 $942.00 $820.00 $885.00 $945.00 $825.00 $894.00 $948.00 $830.00 $903.00 $951.00 $835.00 $912.00 $954.00 $840.00 $921.00 $957.00 $845.00 $930.00 $960.00 $850.00 $939.00 $963.00 $855.00 $948.00 $966.00 $860.00 $957.00 $969.00 $865.00 $966.00 $972.00 $870.00 $975.00 $975.00 $875.00 $984.00 $978.00 $880.00 $993.00 $981.00 $885.00 $1,002.00 $984.00 $890.00 $1,011.00 $987.00 $895.00 $1,020.00 $990.00 $900.00 $1,029.00 $993.00 $905.00 $1,038.00 $996.00 $910.00 $1,047.00 $999.00 $915.00 $1,056.00 $1,002.00 $920.00 $1,065.00 $1,005.00 $925.00 $1,074.00 $1,008.00 $930.00 $1,083.00 $1,011.00 $935.00 $1,092.00 $1,014.00 $940.00 $1,101.00 $1,017.00 $945.00 $1,110.00 $1,020.00 $950.00 $1,119.00 $1,023.00 $955.00 $1,128.00 $1,026.00 $960.00 $1,137.00 $1,029.00 $965.00 $1,146.00 $1,032.00 $970.00 $1,155.00 $1,035.00 $975.00 $1,164.00 $1,038.00 $980.00 $1,173.00 $1,041.00 $985.00 $1,182.00 $1,044.00 $990.00 $1,191.00 $1,047.00 $995.00 $1,200.00 $1,050.00 $1,000.00 $1,209.00 $1,053.00 $1,005.00 $1,218.00 $1,056.00 $1,010.00 $1,227.00 $1,059.00 $1,015.00 $1,236.00 $1,062.00 $1,020.00 $1,245.00 $1,065.00 $1,025.00 $1,254.00 $1,068.00 $1,030.00 $1,263.00 $1,071.00 $1,035.00

A 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228

B 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164

C D E $1,272.00 $1,074.00 $1,040.00 $1,281.00 $1,077.00 $1,045.00 $1,290.00 $1,080.00 $1,050.00 $1,299.00 $1,083.00 $1,055.00 $1,308.00 $1,086.00 $1,060.00 $1,317.00 $1,089.00 $1,065.00 $1,326.00 $1,092.00 $1,070.00 $1,335.00 $1,095.00 $1,075.00 $1,344.00 $1,098.00 $1,080.00 $1,353.00 $1,101.00 $1,085.00 $1,362.00 $1,104.00 $1,090.00 $1,371.00 $1,107.00 $1,095.00 $1,380.00 $1,110.00 $1,100.00 $1,389.00 $1,113.00 $1,105.00 $1,398.00 $1,116.00 $1,110.00 $1,407.00 $1,119.00 $1,115.00 $1,416.00 $1,122.00 $1,120.00 $1,425.00 $1,125.00 $1,125.00 $1,434.00 $1,128.00 $1,130.00 $1,443.00 $1,131.00 $1,135.00 $1,452.00 $1,134.00 $1,140.00 $1,461.00 $1,137.00 $1,145.00 $1,470.00 $1,140.00 $1,150.00 $1,479.00 $1,143.00 $1,155.00 $1,488.00 $1,146.00 $1,160.00 $1,497.00 $1,149.00 $1,165.00 $1,506.00 $1,152.00 $1,170.00 $1,515.00 $1,155.00 $1,175.00 $1,524.00 $1,158.00 $1,180.00 $1,533.00 $1,161.00 $1,185.00 $1,542.00 $1,164.00 $1,190.00 $1,551.00 $1,167.00 $1,195.00 $1,560.00 $1,170.00 $1,200.00 $1,569.00 $1,173.00 $1,205.00 $1,578.00 $1,176.00 $1,210.00 $1,587.00 $1,179.00 $1,215.00 $1,596.00 $1,182.00 $1,220.00 $1,605.00 $1,185.00 $1,225.00 $1,614.00 $1,188.00 $1,230.00 $1,623.00 $1,191.00 $1,235.00 $1,632.00 $1,194.00 $1,240.00 $1,641.00 $1,197.00 $1,245.00 $1,650.00 $1,200.00 $1,250.00 $1,659.00 $1,203.00 $1,255.00 $1,668.00 $1,206.00 $1,260.00 $1,677.00 $1,209.00 $1,265.00 $1,686.00 $1,212.00 $1,270.00 $1,695.00 $1,215.00 $1,275.00 $1,704.00 $1,218.00 $1,280.00 $1,713.00 $1,221.00 $1,285.00 $1,722.00 $1,224.00 $1,290.00 $1,731.00 $1,227.00 $1,295.00 $1,740.00 $1,230.00 $1,300.00 $1,749.00 $1,233.00 $1,305.00 $1,758.00 $1,236.00 $1,310.00 $1,767.00 $1,239.00 $1,315.00 $1,776.00 $1,242.00 $1,320.00

A 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264

B 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200

C D E $1,785.00 $1,245.00 $1,325.00 $1,794.00 $1,248.00 $1,330.00 $1,803.00 $1,251.00 $1,335.00 $1,812.00 $1,254.00 $1,340.00 $1,821.00 $1,257.00 $1,345.00 $1,830.00 $1,260.00 $1,350.00 $1,839.00 $1,263.00 $1,355.00 $1,848.00 $1,266.00 $1,360.00 $1,857.00 $1,269.00 $1,365.00 $1,866.00 $1,272.00 $1,370.00 $1,875.00 $1,275.00 $1,375.00 $1,884.00 $1,278.00 $1,380.00 $1,893.00 $1,281.00 $1,385.00 $1,902.00 $1,284.00 $1,390.00 $1,911.00 $1,287.00 $1,395.00 $1,920.00 $1,290.00 $1,400.00 $1,929.00 $1,293.00 $1,405.00 $1,938.00 $1,296.00 $1,410.00 $1,947.00 $1,299.00 $1,415.00 $1,956.00 $1,302.00 $1,420.00 $1,965.00 $1,305.00 $1,425.00 $1,974.00 $1,308.00 $1,430.00 $1,983.00 $1,311.00 $1,435.00 $1,992.00 $1,314.00 $1,440.00 $2,001.00 $1,317.00 $1,445.00 $2,010.00 $1,320.00 $1,450.00 $2,019.00 $1,323.00 $1,455.00 $2,028.00 $1,326.00 $1,460.00 $2,037.00 $1,329.00 $1,465.00 $2,046.00 $1,332.00 $1,470.00 $2,055.00 $1,335.00 $1,475.00 $2,064.00 $1,338.00 $1,480.00 $2,073.00 $1,341.00 $1,485.00 $2,082.00 $1,344.00 $1,490.00 $2,091.00 $1,347.00 $1,495.00 $2,100.00 $1,350.00 $1,500.00

A B C D E F G 1 PROBLEM 1.24 2 3 a AVERAGE TOTAL COST 4 SQUARE FEET FLOORS TOTAL COST COST PER FLOOR DECREASE 5 6 400,000 1 $112,800,000.00 $112,800,000.00 N/A 7 400,000 2 $73,600,000.00 $36,800,000.00 $39,200,000.00 8 400,000 3 $61,066,666.67 $20,355,555.56 $12,533,333.33 9 400,000 4 $55,200,000.00 $13,800,000.00 $5,866,666.67 10 400,000 5 $52,000,000.00 $10,400,000.00 $3,200,000.00 11 400,000 6 $50,133,333.33 $8,355,555.56 $1,866,666.67 12 400,000 7 $49,028,571.43 $7,004,081.63 $1,104,761.90 13 400,000 8 $48,400,000.00 $6,050,000.00 $628,571.43 14 400,000 9 $48,088,888.89 $5,343,209.88 $311,111.11 15 400,000 10 $48,000,000.00 $4,800,000.00 $88,888.89 *** 16 400,000 11 $48,072,727.27 $4,370,247.93 -$72,727.27 17 400,000 12 $48,266,666.67 $4,022,222.22 -$193,939.39 18 19 b *** OPTIMUM IS 10 FLOORS 20 21 c TC= (200+80X+2(X^2))(400,000/X)NOTE THAT A=400,000/X 22 23 dTC/dX= (80+4X)(400,000/X)+(200+80X+2(X^2))(-400,000/X^2)=0 24 25 800,000-80,000,000/X^2=0 26 27 X^2=80,000,000/800,000=100 28 29 X=10 30 31 THIS AGREES WITH THE 10 FLOORS SPECIFIED IN THE TABLE.

1 26 51 76 101 126 151 176 201 226 251 276 301 326 351 376 401 426 451 476 501 526 551 576 601

A B C D E F G 1 PROBLEM 1.25 2 3 a ENGINE LATHE EQN TC=$7Q 4 TURRET LATHE EQN TC=$120N+5.25Q 5 6 N=1 FOR Q=1 TO 300 7 N=2 FOR Q=301 TO 600, ETC. 8 9 SETTING THE TWO TC EQUATIONS EQUAL FOR N=1, 10 $7Q=$120+$5.25Q 11 1.75Q=120 12 13 Q=120/1.75= 68.57 UNITS USE ENGINE LATHE IF Q=68 OR LESS 14 USE TURRET LATHE IF Q=69 TO 300 15 16 SETTING THE TWO EQUATIONS EQUAL FOR N=2, 17 $7Q=$240+$5.25Q 18 1.75Q=240 19 20 Q=240/1.75= 137.14 UNITS SINCE THIS IS BELOW 301, 21 USE TURRET LATHE IF Q=301 TO 600 22 23 GRAPHICAL REPRESENTATION OF BREAKEVEN POINT 24 THIS GRAPH WAS DEVELOPED FROM THE TABLE OF COSTS AFTER PART c 25 26 27 $4,500.00 28 29 30 $4,000.00 31 32 $3,500.00 33 34 $3,000.00 35 36 $2,500.00 37 ENGINE L 38 39 $2,000.00 TURRET L 40 41 $1,500.00 42 43 $1,000.00 44 45 $500.00 46 47 48 $0.00 49 50 51 52 53 b Q= 68 UNITS 54 N= 1 SETUP 55 TC(ENGINE LATHE)= $476.00 =7*68 56 TC(TURRET LATHE)= $477.00 =120*1+5.25*68 57 USE ENGINE LATHE FOR Q=68

58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114

Q= N= ENGINE LATHE TC= TURRET LATHE TC= SAVINGS WITH TURRET LATHE=

400 UNITS 2 SETUPS $2,800.00 =7*400 $2,340.00 =120*2+5.25*400 $460.00 =2800-2340

BRUTE FORCE TABLE OF COSTS FOR Q FROM 0 TO 600 Q N ENGINE L TURRET L 0 1 $0.00 $120.00 1 1 $7.00 $125.25 2 1 $14.00 $130.50 3 1 $21.00 $135.75 4 1 $28.00 $141.00 5 1 $35.00 $146.25 6 1 $42.00 $151.50 7 1 $49.00 $156.75 8 1 $56.00 $162.00 9 1 $63.00 $167.25 10 1 $70.00 $172.50 11 1 $77.00 $177.75 12 1 $84.00 $183.00 13 1 $91.00 $188.25 14 1 $98.00 $193.50 15 1 $105.00 $198.75 16 1 $112.00 $204.00 17 1 $119.00 $209.25 18 1 $126.00 $214.50 19 1 $133.00 $219.75 20 1 $140.00 $225.00 21 1 $147.00 $230.25 22 1 $154.00 $235.50 23 1 $161.00 $240.75 24 1 $168.00 $246.00 25 1 $175.00 $251.25 26 1 $182.00 $256.50 27 1 $189.00 $261.75 28 1 $196.00 $267.00 29 1 $203.00 $272.25 30 1 $210.00 $277.50 31 1 $217.00 $282.75 32 1 $224.00 $288.00 33 1 $231.00 $293.25 34 1 $238.00 $298.50 35 1 $245.00 $303.75 36 1 $252.00 $309.00 37 1 $259.00 $314.25 38 1 $266.00 $319.50 39 1 $273.00 $324.75 40 1 $280.00 $330.00 41 1 $287.00 $335.25 42 1 $294.00 $340.50 43 1 $301.00 $345.75 44 1 $308.00 $351.00 45 1 $315.00 $356.25 46 1 $322.00 $361.50

C 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103

D 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

E $329.00 $336.00 $343.00 $350.00 $357.00 $364.00 $371.00 $378.00 $385.00 $392.00 $399.00 $406.00 $413.00 $420.00 $427.00 $434.00 $441.00 $448.00 $455.00 $462.00 $469.00 $476.00 $483.00 $490.00 $497.00 $504.00 $511.00 $518.00 $525.00 $532.00 $539.00 $546.00 $553.00 $560.00 $567.00 $574.00 $581.00 $588.00 $595.00 $602.00 $609.00 $616.00 $623.00 $630.00 $637.00 $644.00 $651.00 $658.00 $665.00 $672.00 $679.00 $686.00 $693.00 $700.00 $707.00 $714.00 $721.00

F $366.75 $372.00 $377.25 $382.50 $387.75 $393.00 $398.25 $403.50 $408.75 $414.00 $419.25 $424.50 $429.75 $435.00 $440.25 $445.50 $450.75 $456.00 $461.25 $466.50 $471.75 $477.00 $482.25 $487.50 $492.75 $498.00 $503.25 $508.50 $513.75 $519.00 $524.25 $529.50 $534.75 $540.00 $545.25 $550.50 $555.75 $561.00 $566.25 $571.50 $576.75 $582.00 $587.25 $592.50 $597.75 $603.00 $608.25 $613.50 $618.75 $624.00 $629.25 $634.50 $639.75 $645.00 $650.25 $655.50 $660.75

C 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160

D 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

E $728.00 $735.00 $742.00 $749.00 $756.00 $763.00 $770.00 $777.00 $784.00 $791.00 $798.00 $805.00 $812.00 $819.00 $826.00 $833.00 $840.00 $847.00 $854.00 $861.00 $868.00 $875.00 $882.00 $889.00 $896.00 $903.00 $910.00 $917.00 $924.00 $931.00 $938.00 $945.00 $952.00 $959.00 $966.00 $973.00 $980.00 $987.00 $994.00 $1,001.00 $1,008.00 $1,015.00 $1,022.00 $1,029.00 $1,036.00 $1,043.00 $1,050.00 $1,057.00 $1,064.00 $1,071.00 $1,078.00 $1,085.00 $1,092.00 $1,099.00 $1,106.00 $1,113.00 $1,120.00

F $666.00 $671.25 $676.50 $681.75 $687.00 $692.25 $697.50 $702.75 $708.00 $713.25 $718.50 $723.75 $729.00 $734.25 $739.50 $744.75 $750.00 $755.25 $760.50 $765.75 $771.00 $776.25 $781.50 $786.75 $792.00 $797.25 $802.50 $807.75 $813.00 $818.25 $823.50 $828.75 $834.00 $839.25 $844.50 $849.75 $855.00 $860.25 $865.50 $870.75 $876.00 $881.25 $886.50 $891.75 $897.00 $902.25 $907.50 $912.75 $918.00 $923.25 $928.50 $933.75 $939.00 $944.25 $949.50 $954.75 $960.00

A 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285

C 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217

D 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

E F $1,127.00 $965.25 $1,134.00 $970.50 $1,141.00 $975.75 $1,148.00 $981.00 $1,155.00 $986.25 $1,162.00 $991.50 $1,169.00 $996.75 $1,176.00 $1,002.00 $1,183.00 $1,007.25 $1,190.00 $1,012.50 $1,197.00 $1,017.75 $1,204.00 $1,023.00 $1,211.00 $1,028.25 $1,218.00 $1,033.50 $1,225.00 $1,038.75 $1,232.00 $1,044.00 $1,239.00 $1,049.25 $1,246.00 $1,054.50 $1,253.00 $1,059.75 $1,260.00 $1,065.00 $1,267.00 $1,070.25 $1,274.00 $1,075.50 $1,281.00 $1,080.75 $1,288.00 $1,086.00 $1,295.00 $1,091.25 $1,302.00 $1,096.50 $1,309.00 $1,101.75 $1,316.00 $1,107.00 $1,323.00 $1,112.25 $1,330.00 $1,117.50 $1,337.00 $1,122.75 $1,344.00 $1,128.00 $1,351.00 $1,133.25 $1,358.00 $1,138.50 $1,365.00 $1,143.75 $1,372.00 $1,149.00 $1,379.00 $1,154.25 $1,386.00 $1,159.50 $1,393.00 $1,164.75 $1,400.00 $1,170.00 $1,407.00 $1,175.25 $1,414.00 $1,180.50 $1,421.00 $1,185.75 $1,428.00 $1,191.00 $1,435.00 $1,196.25 $1,442.00 $1,201.50 $1,449.00 $1,206.75 $1,456.00 $1,212.00 $1,463.00 $1,217.25 $1,470.00 $1,222.50 $1,477.00 $1,227.75 $1,484.00 $1,233.00 $1,491.00 $1,238.25 $1,498.00 $1,243.50 $1,505.00 $1,248.75 $1,512.00 $1,254.00 $1,519.00 $1,259.25

A 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342

C 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274

D 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

E F $1,526.00 $1,264.50 $1,533.00 $1,269.75 $1,540.00 $1,275.00 $1,547.00 $1,280.25 $1,554.00 $1,285.50 $1,561.00 $1,290.75 $1,568.00 $1,296.00 $1,575.00 $1,301.25 $1,582.00 $1,306.50 $1,589.00 $1,311.75 $1,596.00 $1,317.00 $1,603.00 $1,322.25 $1,610.00 $1,327.50 $1,617.00 $1,332.75 $1,624.00 $1,338.00 $1,631.00 $1,343.25 $1,638.00 $1,348.50 $1,645.00 $1,353.75 $1,652.00 $1,359.00 $1,659.00 $1,364.25 $1,666.00 $1,369.50 $1,673.00 $1,374.75 $1,680.00 $1,380.00 $1,687.00 $1,385.25 $1,694.00 $1,390.50 $1,701.00 $1,395.75 $1,708.00 $1,401.00 $1,715.00 $1,406.25 $1,722.00 $1,411.50 $1,729.00 $1,416.75 $1,736.00 $1,422.00 $1,743.00 $1,427.25 $1,750.00 $1,432.50 $1,757.00 $1,437.75 $1,764.00 $1,443.00 $1,771.00 $1,448.25 $1,778.00 $1,453.50 $1,785.00 $1,458.75 $1,792.00 $1,464.00 $1,799.00 $1,469.25 $1,806.00 $1,474.50 $1,813.00 $1,479.75 $1,820.00 $1,485.00 $1,827.00 $1,490.25 $1,834.00 $1,495.50 $1,841.00 $1,500.75 $1,848.00 $1,506.00 $1,855.00 $1,511.25 $1,862.00 $1,516.50 $1,869.00 $1,521.75 $1,876.00 $1,527.00 $1,883.00 $1,532.25 $1,890.00 $1,537.50 $1,897.00 $1,542.75 $1,904.00 $1,548.00 $1,911.00 $1,553.25 $1,918.00 $1,558.50

A 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399

C 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331

D 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

E F $1,925.00 $1,563.75 $1,932.00 $1,569.00 $1,939.00 $1,574.25 $1,946.00 $1,579.50 $1,953.00 $1,584.75 $1,960.00 $1,590.00 $1,967.00 $1,595.25 $1,974.00 $1,600.50 $1,981.00 $1,605.75 $1,988.00 $1,611.00 $1,995.00 $1,616.25 $2,002.00 $1,621.50 $2,009.00 $1,626.75 $2,016.00 $1,632.00 $2,023.00 $1,637.25 $2,030.00 $1,642.50 $2,037.00 $1,647.75 $2,044.00 $1,653.00 $2,051.00 $1,658.25 $2,058.00 $1,663.50 $2,065.00 $1,668.75 $2,072.00 $1,674.00 $2,079.00 $1,679.25 $2,086.00 $1,684.50 $2,093.00 $1,689.75 $2,100.00 $1,695.00 $2,107.00 $1,820.25 $2,114.00 $1,825.50 $2,121.00 $1,830.75 $2,128.00 $1,836.00 $2,135.00 $1,841.25 $2,142.00 $1,846.50 $2,149.00 $1,851.75 $2,156.00 $1,857.00 $2,163.00 $1,862.25 $2,170.00 $1,867.50 $2,177.00 $1,872.75 $2,184.00 $1,878.00 $2,191.00 $1,883.25 $2,198.00 $1,888.50 $2,205.00 $1,893.75 $2,212.00 $1,899.00 $2,219.00 $1,904.25 $2,226.00 $1,909.50 $2,233.00 $1,914.75 $2,240.00 $1,920.00 $2,247.00 $1,925.25 $2,254.00 $1,930.50 $2,261.00 $1,935.75 $2,268.00 $1,941.00 $2,275.00 $1,946.25 $2,282.00 $1,951.50 $2,289.00 $1,956.75 $2,296.00 $1,962.00 $2,303.00 $1,967.25 $2,310.00 $1,972.50 $2,317.00 $1,977.75

A 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456

C 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388

D 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

E F $2,324.00 $1,983.00 $2,331.00 $1,988.25 $2,338.00 $1,993.50 $2,345.00 $1,998.75 $2,352.00 $2,004.00 $2,359.00 $2,009.25 $2,366.00 $2,014.50 $2,373.00 $2,019.75 $2,380.00 $2,025.00 $2,387.00 $2,030.25 $2,394.00 $2,035.50 $2,401.00 $2,040.75 $2,408.00 $2,046.00 $2,415.00 $2,051.25 $2,422.00 $2,056.50 $2,429.00 $2,061.75 $2,436.00 $2,067.00 $2,443.00 $2,072.25 $2,450.00 $2,077.50 $2,457.00 $2,082.75 $2,464.00 $2,088.00 $2,471.00 $2,093.25 $2,478.00 $2,098.50 $2,485.00 $2,103.75 $2,492.00 $2,109.00 $2,499.00 $2,114.25 $2,506.00 $2,119.50 $2,513.00 $2,124.75 $2,520.00 $2,130.00 $2,527.00 $2,135.25 $2,534.00 $2,140.50 $2,541.00 $2,145.75 $2,548.00 $2,151.00 $2,555.00 $2,156.25 $2,562.00 $2,161.50 $2,569.00 $2,166.75 $2,576.00 $2,172.00 $2,583.00 $2,177.25 $2,590.00 $2,182.50 $2,597.00 $2,187.75 $2,604.00 $2,193.00 $2,611.00 $2,198.25 $2,618.00 $2,203.50 $2,625.00 $2,208.75 $2,632.00 $2,214.00 $2,639.00 $2,219.25 $2,646.00 $2,224.50 $2,653.00 $2,229.75 $2,660.00 $2,235.00 $2,667.00 $2,240.25 $2,674.00 $2,245.50 $2,681.00 $2,250.75 $2,688.00 $2,256.00 $2,695.00 $2,261.25 $2,702.00 $2,266.50 $2,709.00 $2,271.75 $2,716.00 $2,277.00

A 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513

C 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445

D 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

E F $2,723.00 $2,282.25 $2,730.00 $2,287.50 $2,737.00 $2,292.75 $2,744.00 $2,298.00 $2,751.00 $2,303.25 $2,758.00 $2,308.50 $2,765.00 $2,313.75 $2,772.00 $2,319.00 $2,779.00 $2,324.25 $2,786.00 $2,329.50 $2,793.00 $2,334.75 $2,800.00 $2,340.00 $2,807.00 $2,345.25 $2,814.00 $2,350.50 $2,821.00 $2,355.75 $2,828.00 $2,361.00 $2,835.00 $2,366.25 $2,842.00 $2,371.50 $2,849.00 $2,376.75 $2,856.00 $2,382.00 $2,863.00 $2,387.25 $2,870.00 $2,392.50 $2,877.00 $2,397.75 $2,884.00 $2,403.00 $2,891.00 $2,408.25 $2,898.00 $2,413.50 $2,905.00 $2,418.75 $2,912.00 $2,424.00 $2,919.00 $2,429.25 $2,926.00 $2,434.50 $2,933.00 $2,439.75 $2,940.00 $2,445.00 $2,947.00 $2,450.25 $2,954.00 $2,455.50 $2,961.00 $2,460.75 $2,968.00 $2,466.00 $2,975.00 $2,471.25 $2,982.00 $2,476.50 $2,989.00 $2,481.75 $2,996.00 $2,487.00 $3,003.00 $2,492.25 $3,010.00 $2,497.50 $3,017.00 $2,502.75 $3,024.00 $2,508.00 $3,031.00 $2,513.25 $3,038.00 $2,518.50 $3,045.00 $2,523.75 $3,052.00 $2,529.00 $3,059.00 $2,534.25 $3,066.00 $2,539.50 $3,073.00 $2,544.75 $3,080.00 $2,550.00 $3,087.00 $2,555.25 $3,094.00 $2,560.50 $3,101.00 $2,565.75 $3,108.00 $2,571.00 $3,115.00 $2,576.25

A 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570

C 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502

D 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

E F $3,122.00 $2,581.50 $3,129.00 $2,586.75 $3,136.00 $2,592.00 $3,143.00 $2,597.25 $3,150.00 $2,602.50 $3,157.00 $2,607.75 $3,164.00 $2,613.00 $3,171.00 $2,618.25 $3,178.00 $2,623.50 $3,185.00 $2,628.75 $3,192.00 $2,634.00 $3,199.00 $2,639.25 $3,206.00 $2,644.50 $3,213.00 $2,649.75 $3,220.00 $2,655.00 $3,227.00 $2,660.25 $3,234.00 $2,665.50 $3,241.00 $2,670.75 $3,248.00 $2,676.00 $3,255.00 $2,681.25 $3,262.00 $2,686.50 $3,269.00 $2,691.75 $3,276.00 $2,697.00 $3,283.00 $2,702.25 $3,290.00 $2,707.50 $3,297.00 $2,712.75 $3,304.00 $2,718.00 $3,311.00 $2,723.25 $3,318.00 $2,728.50 $3,325.00 $2,733.75 $3,332.00 $2,739.00 $3,339.00 $2,744.25 $3,346.00 $2,749.50 $3,353.00 $2,754.75 $3,360.00 $2,760.00 $3,367.00 $2,765.25 $3,374.00 $2,770.50 $3,381.00 $2,775.75 $3,388.00 $2,781.00 $3,395.00 $2,786.25 $3,402.00 $2,791.50 $3,409.00 $2,796.75 $3,416.00 $2,802.00 $3,423.00 $2,807.25 $3,430.00 $2,812.50 $3,437.00 $2,817.75 $3,444.00 $2,823.00 $3,451.00 $2,828.25 $3,458.00 $2,833.50 $3,465.00 $2,838.75 $3,472.00 $2,844.00 $3,479.00 $2,849.25 $3,486.00 $2,854.50 $3,493.00 $2,859.75 $3,500.00 $2,865.00 $3,507.00 $2,870.25 $3,514.00 $2,875.50

A 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627

C 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559

D 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

E F $3,521.00 $2,880.75 $3,528.00 $2,886.00 $3,535.00 $2,891.25 $3,542.00 $2,896.50 $3,549.00 $2,901.75 $3,556.00 $2,907.00 $3,563.00 $2,912.25 $3,570.00 $2,917.50 $3,577.00 $2,922.75 $3,584.00 $2,928.00 $3,591.00 $2,933.25 $3,598.00 $2,938.50 $3,605.00 $2,943.75 $3,612.00 $2,949.00 $3,619.00 $2,954.25 $3,626.00 $2,959.50 $3,633.00 $2,964.75 $3,640.00 $2,970.00 $3,647.00 $2,975.25 $3,654.00 $2,980.50 $3,661.00 $2,985.75 $3,668.00 $2,991.00 $3,675.00 $2,996.25 $3,682.00 $3,001.50 $3,689.00 $3,006.75 $3,696.00 $3,012.00 $3,703.00 $3,017.25 $3,710.00 $3,022.50 $3,717.00 $3,027.75 $3,724.00 $3,033.00 $3,731.00 $3,038.25 $3,738.00 $3,043.50 $3,745.00 $3,048.75 $3,752.00 $3,054.00 $3,759.00 $3,059.25 $3,766.00 $3,064.50 $3,773.00 $3,069.75 $3,780.00 $3,075.00 $3,787.00 $3,080.25 $3,794.00 $3,085.50 $3,801.00 $3,090.75 $3,808.00 $3,096.00 $3,815.00 $3,101.25 $3,822.00 $3,106.50 $3,829.00 $3,111.75 $3,836.00 $3,117.00 $3,843.00 $3,122.25 $3,850.00 $3,127.50 $3,857.00 $3,132.75 $3,864.00 $3,138.00 $3,871.00 $3,143.25 $3,878.00 $3,148.50 $3,885.00 $3,153.75 $3,892.00 $3,159.00 $3,899.00 $3,164.25 $3,906.00 $3,169.50 $3,913.00 $3,174.75

A 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668

C 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600

D 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

E F $3,920.00 $3,180.00 $3,927.00 $3,185.25 $3,934.00 $3,190.50 $3,941.00 $3,195.75 $3,948.00 $3,201.00 $3,955.00 $3,206.25 $3,962.00 $3,211.50 $3,969.00 $3,216.75 $3,976.00 $3,222.00 $3,983.00 $3,227.25 $3,990.00 $3,232.50 $3,997.00 $3,237.75 $4,004.00 $3,243.00 $4,011.00 $3,248.25 $4,018.00 $3,253.50 $4,025.00 $3,258.75 $4,032.00 $3,264.00 $4,039.00 $3,269.25 $4,046.00 $3,274.50 $4,053.00 $3,279.75 $4,060.00 $3,285.00 $4,067.00 $3,290.25 $4,074.00 $3,295.50 $4,081.00 $3,300.75 $4,088.00 $3,306.00 $4,095.00 $3,311.25 $4,102.00 $3,316.50 $4,109.00 $3,321.75 $4,116.00 $3,327.00 $4,123.00 $3,332.25 $4,130.00 $3,337.50 $4,137.00 $3,342.75 $4,144.00 $3,348.00 $4,151.00 $3,353.25 $4,158.00 $3,358.50 $4,165.00 $3,363.75 $4,172.00 $3,369.00 $4,179.00 $3,374.25 $4,186.00 $3,379.50 $4,193.00 $3,384.75 $4,200.00 $3,390.00

H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38ENGINE L 39 TURRET L 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57

H 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114

A B 1 PROBLEM 1.26 2 3 PRODUCTION CAPACITY = 4 PERCENT OF CAPACITY NOW= 5 IF PERCENT OF CAPACITY= 6 SELLING PRICE/PALLET= 7 VARIABLE COST/PALLET= 8 FIXED COST= 9 10 a ANNUAL PROFIT= 11 12 13 b LET X= 14 ANNUAL PROFIT= 15 X=BREAKEVEN SALES VOLUME 16 17 c ANNUAL PROFIT AT 90% CAP= 18 19 d LET Y= 20 % REDUCTION IN FIXED COSTS= 21 ANNUAL PROFIT= 22 Y=BREAKEVEN SALES VOLUME=

300,000 70.00% 90.00% $18.25 $15.75 $550,000.00 -$25,000.00 (OR LOSS OF $25,000.00) =300000*70%*(18.25-15.75)-550000 BREAKEVEN SALES VOLUME $0.00 =X*(18.75-15.25)-550000 220,000 =550000/(18.25-15.75) $125,000.00 =300000*90%*(18.25-15.75)-550000 BREAKEVEN SALES VOLUME 40% $0.00 =Y*(18.25-15.75)-550000*(1-40%) 132,000 =550000*(1-40%)/(18.25-15.75)

A B C D E F G H 1 PROBLEM 1.27 2 3 SEQUENCE 1 W1 W2 W3 W4 W5 4 SCRAP RATE 3.00% 5.00% 5.00% 4.00% 4.00% 5 6 SEQUENCE 2 WA WB WC 7 SCRAP RATE 5.00% 3.00% 3.00% 8 9 LOT SIZE= 1,000 10 RAW MAT'L COST= $30.00 11 SEQUENCING COST A= $180.00 PER UNIT 12 SEQUENCING COST B= $210.00 PER UNIT 13 14 PERCENT GOOD FROM SEQ 1= 80.6792% =(1-0.03)*(1-0.05)*(1-0.05)*(1-0.04)*(1-0.04) 15 PERCENT GOOD FROM SEQ 2= 89.3855% =(1-0.05)*(1-0.03)*(1-0.03) 16 17 18 SEQUENCE A TC= $210,000.00 =1000*(30+180) 19 SEQUENCE A TC/GOOD UNIT= $260.29 =210000/(1000*80.6792%) 20 21 SEQUENCE B TC= $240,000.00 =1000*(30+210) 22 SEQUENCE B TC/GOOD UNIT= $268.50 =240000/(1000*89.3855%) 23 24 25 SEQUENCE A HAS A LOWER TC/GOOD UNIT 26 27 SIDE NOTE! THESE SCRAP RATES ARE TERRIBLE. 28 THIS COMPANY WILL NOT BE COMPETITIVE

A 1 PROBLEM 1.28 2 3 a 4 5 6 7 8 9 10 11 12 13 14 15 b 16

FC/MONTH MPG MAINT COST PER MI

CAR A $550 25 $0.20

CAR B $400 19 $0.25

CAR C $800 33 $0.15

MILES/MONTH=

4,000

COST OF FUEL/GAL=

$3.25

COST/MONTH= CALC FOR CAR A= AVG COST/MILE= CALC FOR CAR C=

$1,870.00 $2,084.21 $1,793.94 =550+(4000/25)*3.25+4000*0.2 $0.47

$0.52

$0.45 =1793.94/4000

A 1 PROBLEM 1.29 2 3 4 5 6 7 8 9 10 11 12 a 13 14 15 16 17 18 19 20 21 22 23 b

TAYLOR'S TOOL LIFE EXPONENT = TOOL CHANGE TIME, MINUTES = COST $/CUTTING EDGE = COST OF LABOR AND OH $/MIN = CONSTANT =

n tc cc co K

TUNGSTEN COATED CARBIDE CARBIDE CERAMIC INSERT INSERT INSERT 0.22 0.27 0.38 2 2 2 $0.40 $1.80 $3.00 $1.00 $1.00 $1.00 150 250 550

MIN UNIT COST TOTAL TOOL LIFE = Tc= 8.509 10.274 8.158 CALCULATION 1 =(2+0.4/1)*((1/0.22)-1) CALCULATION 2 =(2+1.8/1)*((1/0.27)-1) CALCULATION 3 =(2+3/1)*((1/0.38)-1)

CUTTING SPEED = CALCULATION 1 CALCULATION 2 CALCULATION 3

V= 93.652 133.281 247.721 =150/(8.509^0.22) =250/(10.274^0.27) =550/(8.158^0.38)

BASED ON V, THE CERAMIC INSERT IS PREFERRED AT 247.721 FEET/MINUTE

A B C D 1 PROBLEM 1.30 2 3 4 MACHINE A MACHINE B 5 TOTAL SETUP TIME IN HOURS = 4 6 6 CALCULATION =8*0.75 7 MACHINING TIME PER UNIT = 0.50 0.55 8 HOURLY WAGE RATES = $20.00 $18.00 9 HOURLY OVERHEAD RATES = $30.00 $27.00 10 11 a ORDER SIZE = 100 12 COST OF ORDER SIZE = $2,700.00 $2,745.00 13 CALCULATIONS =4*(20+30)+100*0.5*(20+30) =6*(18+27)+100*0.55*(18+27) 14 15 b ORDER SIZE = 500 16 COST OF ORDER SIZE = $12,700.00 $12,645.00 17 CALCULATIONS =4*(20+30)+500*0.50*(20+30) =6*(18+27)+500*0.55*(18+27) 18 19 c LET X= BREAKEVEN ORDER QUANTITY 20 21 EQUATE THE COSTS OF MACHINES A AND B 22 4*(20+30)+X*0.5*(20+30)=6*(18+27)+X*0.55*(18+27) 23 24 SOLVE FOR X 25 X*(0.5*(20+30)-0.55*(18+27))=6*(18+27)-4*(20+30) 26 0.25*X= 70 27 X= 280

NOTES - CHAPTER 2 SOLUTIONS FOLLOWING ARE SOME THOUGHTS ABOUT THE PROBLEMS AND SOLUTIONS IN THIS CHAPTER THAT MAY BE OF HELP TO FACULTY AND STUDENTS. 1

THIS IS, PERHAPS, THE MOST CRITICAL CHAPTER IN THE BOOK IN THAT IT DEALS WITH THE "TIME VALUE OF MONEY (TVM)," A FUNDAMENTAL CONCEPT USED THROUGHOUT THE REST OF THE BOOK.

THERE ARE 180 BASE PROBLEMS, MANY WITH MULTIPLE PARTS, AND MULTIPLE SOLUTIONS FOR MANY OF THOSE PARTS ARE PRESENTED IN THIS SOLUTION MANUAL

THERE ARE FIVE DIFFERENT METHODS THAT ARE SEEN MULTIPLE TIMES IN THESE SOLUTIONS. THEY INCLUDE USE OF (1) SIMPLE AND COMPOUND INTEREST FORMULAS, (2) INTEREST TABLES SUCH AS THOSE IN APPENDICES A AND B, AS WELL AS "ELECTRONIC" INTEREST TABLES (SEE ITEM 5 BELOW), (3) USE OF MYRIAD EXCEL FUNCTIONS, (4) SEARCH PROCEDURES USING EXCEL'S "SOLVER" AND "GOAL SEEK" TOOLS, AND (5) BRUTE FORCE TABULAR APPROACHES

THE COMPOUND INTEREST FORMULAS ARE OFTEN THE MOST ONEROUS TO USE, GIVEN THAT THEY REPRESENT THE FUNDAMENTAL MATHEMATICS OF TVOM.

THE INTEREST TABLES REPRESENT THE MOST COMMON APPROACH USED HERETOFORE IN "ENGINEERING ECONOMY" COURSES; THEY USUALLY VASTLY SIMPLIFY THE MATHEMATICS INVOLVED BY INCORPORATING ONE OR MORE COMPOUND INTEREST FORMULAS INTO A SINGLE TABULATED "FACTOR" AVAILABLE IN APPENDICES A AND B. SINCE THE INTEREST TABLES ARE FOR ONLY A FINITE (ALTHOUGH VERY LARGE) SET OF INTEREST RATES (i AND j) AND TIME HORIZONS (n), THEY MAY NOT BE AVAILABLE FOR A SPECIFIC SET OF i, j, OR n NEEDED. "ELECTRONIC" INTEREST TABLES ARE AVAILABLE, AND HAVE BEEN USED WHEN UNAVAILABLE TABULATED VALUES OF i, j, AND/OR n HAVE BEEN NEEDED. PLEASE SEE NOTES 13 AND 14 BELOW FOR MORE DETAIL ON THE USE OF "ELECTRONIC" INTEREST TABLES.

PROBLEMS 25, 63, 92, 123, AND 146 ASK FOR THE DEVELOPMENT OF CERTAIN INTEREST FACTORS SUCH AS ARE PRESENTED IN THE INTEREST TABLES. THESE SERVE TO CONVINCE THE STUDENT THAT THERE IS NO "MAGIC" INVOLVED IN THE INTEREST TABLES. IN ADDITION, THE FORMULAS USED IN DEVELOPING THE INTEREST FACTORS HAVE BEEN VERY USEFUL TO THE AUTHORS IN "COPY AND PASTE" OPERATIONS IN THE DEVELOPMENT OF THE CHAPTER 2 SOLUTIONS.

THE EXCEL FUNCTIONS HAVE NOT TRADITIONALLY BEEN WIDELY USED IN TEACHING "ENGINEERING ECONOMY." THEY HAVE, HOWEVER, BEEN USED IN THE WORLD OF FINANCE. THE EXCEL FUNCTIONS ARE WELL DESIGNED, AND PROVIDE A VERY PRECISE TOOL FOR USE IN SOLVING A WIDE ARRAY OF PROBLEMS INVOLVING TVM. BEWARE! FOR THE NOVICE, THESE EXCEL FUNCTIONS MAY APPEAR CONFUSING, COMPLEX, AND NOT WORTH THE TIME TO LEARN. THEY ARE, HOWEVER, QUITE STRAIGHTFORWARD AND CONSISTENT, ONCE ONE GETS PAST THE INITIAL TRIALS OF LEARNING SOMETHING NEW. THEY ARE LIKELY TO BE YOUR FAVORITE METHOD OF PROBLEM SOLUTION IF YOU USE THEM TO SOLVE OR CHECK YOUR SOLUTIONS IN THIS CHAPTER.

SOMETIMES, YOU WILL NEED TO SOLVE FOR A MONETARY VALUE, AN INTEREST RATE, A TIME INTERVAL, A GRADIENT, OR WHATEVER, NEEDED TO MATCH OTHER PARAMETERS OF A PROBLEM (E.G., WHAT INTEREST RATE MAKES AN INVESTMENT OF $100 WORTH $150 IN THREE YEARS). WHILE IT IS OFTEN POSSIBLE AND CONVENIENT TO USE ANALYTICAL APPROACHES (E.G., ALGEBRA), SOMETIMES THESE SOLUTIONS ARE DIFFICULT AND CUMBERSOME (ANALYTICALLY INTRACTABLE OR NEARLY SO). SEARCH PROCEDURES CAN BE VERY HANDY IN THESE CASES. EXCEL PROVIDES "SOLVER" AND "GOAL SEEK," BOTH OF WHICH RECEIVE SOME USE IN THE SOLUTIONS FOR CHAPTER 2. THE AUTHORS HAVE FOUND SOLVER TO BE QUITE ROBUST AND ACCURATE FOR THE PROBLEMS OF CHAPTER 2. GOAL SEEK, ALTHOUGH CLOSE, IS NOT QUITE AS CONSISTENT. BOTH ARE EASY TO USE.

THE "BRUTE FORCE" TABULAR APPROACH CAN BE VERY USEFUL WHEN A PROBLEM IS VERY COMPLEX AND DIFFICULT TO KEEP IN MIND WHILE ATTEMPTING TO USE AN INTEREST TABLE APPROACH OR AN EXCEL FUNCTION APPROACH. IN THESE INSTANCES, IT IS OFTEN USEFUL TO SIMPLY LIST THE ENTIRE SET OF CASH FLOWS, PERIOD BY PERIOD. THEN, OFTEN AN NPV FUNCTION OR AN FV-PLUS-NPV FUNCTION OR A PMT-PLUS-NPV FUNCTION CAN BE EASILY USED ON THE TABLE. THE BRUTE FORCE TABULAR APPROACH ALSO HAS THE ADVANTAGE THAT THE ENTIRE PATTERN OF CASH FLOWS CAN BE SEEN AND UNDERSTOOD. BE CAREFUL! ACTUALLY, MOST PROBLEMS CAN BE SOLVED USING THE BRUTE FORCE APPROACH - IN FACT, IT IS QUITE COMMONLY USED IN INDUSTRY! FOR NOW, WHILE LEARNING THIS MATERIAL, USE THE BRUTE FORCE APPROACH ONLY AS A LAST RESORT OR AS A PROBLEM CHECK AS HAS BEEN DONE IN THESE SOLUTIONS. TO USE THE BRUTE FORCE APPROACH ALONE IN CHAPTER 2 IS TO NOT LEARN THE OTHER APPROACHES.

IN THIS CHAPTER, WITH MULTIPLE APPROACHES USED IN SOLVING MANY PROBLEMS, THERE ARE OFTEN SLIGHTLY DIFFERENT SOLUTIONS ACHIEVED. THESE ARE NOT WRONG! USUALLY, IF NOT ALWAYS, THE INTEREST FORMULA APPROACH AND THE EXCEL FUNCTION APPROACH WILL BE PRECISELY THE SAME BECAUSE THERE IS VIRTUALLY NO ROUND OFF ERROR WITHIN THE COMPUTER. THE INTEREST TABLE APPROACH WILL BE SLIGHTLY DIFFERENT, DUE TO THE PRESENTATION OF INTEREST FACTORS TO FIVE PLACES AFTER THE DECIMAL IN MOST CASES. MANY TABLES USE ONLY FOUR PLACES. EVEN WITH FIVE PLACES, THERE WILL BE SOME MINOR DISCREPANCIES WHEN COMPARED TO THE EVEN MORE PRECISE APPROACHES. NOTE THAT SUCH DIFFERENCES ARE ALMOST ALWAYS INCONSEQUENTIAL BECAUSE THE ESTIMATES REQUIRED IN ECONOMIC EVALUATIONS ARE USUALLY ONLY APPROXIMATIONS ANYWAY.

EVEN THOUGH MANY PROBLEMS HAVE MULTIPLE PARTS, IT IS NOT INTENDED THAT ALL PARTS OF A PROBLEM NECESSARILY BE ASSIGNED AND WORKED. IN MANY CASES, THE LEARNING THAT TAKES PLACE CAN BE ACHIEVED BY WORKING ONLY ONE OR TWO PARTS. SEE, FOR EXAMPLE, PROBLEM 79.

WHILE MULTIPLE APPROACHES ARE OFTEN USED HEREIN TO SOLVE A PROBLEM, KEEP IN MIND THAT THERE ARE AN INFINITE (LITERALLY) NUMBER OF WAYS A TVM PROBLEM CAN BE SET UP AND SOLVED. TRANSLATION - THE SOLUTIONS PRESENTED HEREIN ARE QUITE DIRECT IN THEIR APPROACH, BUT NOT THE ONLY APPROACH.

WHEN A SOLUTION MAKES USE OF BOTH INTEREST TABLES AND EXCEL FUNCTIONS, THE ANSWERS WILL OFTEN BE SOMEWHAT DIFFERENT DUE TO ROUNDOFF ERROR IN THE BOOK TABLES. IN GENERAL, THE EXCEL FUNCTIONS CARRY MANY PLACES WITHIN THE COMPUTER, THEREBY MAKING THEM "EXACT" (REMEMBER, SINCE MOST THINGS IN ENGINEERING ECONOMIC ANALYSIS ARE ESTIMATED, IT IS SOMEWHAT LUDICROUS TO REFER TO MANY SOLUTIONS AS "EXACT"). SOMEWHERE IN BETWEEN THE PRECISION OF EXCEL FUNCTIONS AND THE BOOK'S TABLES ARE "ELECTRONIC" INTEREST TABLES. A SEPARATE WORKSHEET WITH ELECTRONIC INTEREST TABLES IS AVAILABLE ON THE BOOK WEB SITE. USING THAT WORKSHEET, THE USER MAY SELECT THE NUMBER OF PLACES FOLLOWING THE DECIMAL TO USE. HERE IS THE PROTOCOL FOLLOWED IN THE SOLUTIONS TO CHAPTER 2:

IF THE VALUES OF i, j, AND n NEEDED ARE AVAILABLE IN THE BOOK'S TABLES, THEY ARE USED HEREIN TO EMULATE THE PROCEDURE USED BY SOMEONE USING THEM, THIS IS THE TRADITIONAL APPROACH TO ENGINEERING ECONOMIC ANALYSIS. NOTE THAT MOST FACTORS ARE PRESENTED TO 5 PLACES AFTER THE DECIMAL.

IF THE VALUES OF i, j, AND n NEEDED ARE NOT AVAILABLE IN THE BOOK'S TABLES, THE ELECTRONIC TABLES ARE USED. IN THIS CASE, THE NUMBER OF PLACES AFTER THE DECIMAL MUST BE DECIDED UPON FOR BOTH THE INPUT VALUES OF i AND/OR j AND ALSO FOR THE FACTOR VALUE ITSELF. HEREIN, 9 PLACES FOLLOWING THE DECIMAL ARE USED IN ALL CASES. THE REASON FOR 9 PLACES IS THAT THIS NUMBER IS SIMILAR TO THE NUMBER OF PLACES AVAILABLE ON MANY SCIENTIFIC AND FINANCIAL CALCULATORS.

AS A FIRST EXAMPLE, LET'S DETERMINE THE MONTHLY PAYMENT THAT IS EQUIVALENT TO A PRESENT VALUE OF $10,000 IF INTEREST IS 6% NOMINAL, COMPOUNDED MONTHLY OVER A PERIOD OF 24 MONTHS. P= $10,000.00 n= 24 MONTHS r= 6% NOMINAL COMPOUNDED MONTHLY i= 0.500000000% PER MONTH INTEREST TABLE APPROACH: A= =$10,000*(A|P 6%/12,24) =$10,000*(A|P 0.5%,24) =10000*0.04432 $443.20 ELECTRONIC INTEREST TABLE APPROACH: A= =$10,000*(A|P 6%/12,24) =$10,000*(A|P 0.5%,24) =10000*0.044320610 $443.21 EXCEL PMT FUNCTION APPROACH: A= =PMT(6%/12,24,-10000) $443.21

NOTE THAT THE INTEREST TABLE APPROACH SOLUTION IS SLIGHTLY DIFFERENT ($0.01) FROM THE OTHER TWO APPROACHES. WHILE THIS IS INCONSEQUENTIAL, THE DISCREPANCY MAY BE MUCH LARGER, IN ABSOLUTE TERMS, DEPENDING UPON THE MONETARY FIGURES INVOLVED, THE NUMBER OF FACTORS INVOLVED, THE SPECIFIC INTEREST RATES INVOLVED, AND SO ON. d

AS A SECOND EXAMPLE, LET'S DETERMINE THE MONTHLY PAYMENT THAT IS EQUIVALENT TO A PRESENT VALUE OF $10,000 IF INTEREST IS 7% NOMINAL, COMPOUNDED MONTHLY OVER A PERIOD OF 24 MONTHS. P= $10,000.00 n= 24 MONTHS r= 7% NOMINAL COMPOUNDED MONTHLY i= 0.583333333% PER MONTH INTEREST TABLE APPROACH: A= =$10,000*(A|P 7%/12,24) OOPS! THERE IS NO BOOK INTEREST TABLE FOR 7%/12 = 0.583333333% ELECTRONIC INTEREST TABLE APPROACH: A= =$10,000*(A|P 7%/12,24) =$10,000*(A|P 0.583333333%,24) =10000*0.044772579 $447.73 EXCEL PMT FUNCTION APPROACH: A= =PMT(7%/12,24,-10000) $447.73 NOTE THAT THE INTEREST TABLE APPROACH WAS NOT USED. IT MIGHT BE SUGGESTED THAT LINEAR INTERPOLATION BE USED BETWEEN TWO TABULATED INTEREST RATES; HOWEVER, THE INTEREST FACTORS ARE NOT LINEAR, AND INTERPOLATION OFTEN INVITES UNNECESSARY ERRORS. THE TWO APPROACHES USED DID ACHIEVE THE SAME ANSWER. THIS WILL OFTEN, BUT NOT ALWAYS, BE THE CASE DUE TO THE FACT THAT THE EXCEL FUNCTIONS ARE CARRYING MORE PLACES AFTER THE DECIMAL IN THE COMPUTER THAN THE 9 PLACES USED HERE WITH THE ELECTRONIC INTEREST TABLE APPROACH.

THE ELECTRONIC INTEREST TABLE SETUP USED HERE IS MODIFIED TO THE USER'S OWN TASTE, SPECIFICALLY TO PERMIT THE USE OF 9 PLACES AFTER THE DECIMAL FOR i, j, AND THE FACTOR VALUES. PLEASE SEE THE FOLLOWING.

A B 1 PROBLEM 2.1 2 3 DCF STANDS FOR "DISCOUNTED CASH FLOW." 4 5 THE MOVEMENT OF MONEY FORWARD OR BACKWARD IN TIME 6 AN EXPLICIT METHOD FOR CONSIDERING THE TIME VALUE OF MONEY

A B 1 PROBLEM 2.2 2 FOUR DCF RULES: 3 4 1. MONEY HAS A TIME VALUE 5 2. MONEY CANNOT BE ADDED OR SUBTRACTED UNLESS IT OCCURS AT THE SAME POINT(S) IN TIME 6 3. TO MOVE MONEY FORWARD ONE TIME UNIT, MULTIPLY TIMES ONE PLUS THE DISCOUNT OR INTEREST RATE 7 4. TO MOVE MONEY BACKWARD ONE TIME UNIT, DIVIDE BY ONE PLUS THE DISCOUNT OR INTEREST RATE 8

A 1 PROBLEM 2.3 2

3 4 5 6 7 8 9 10

THE OFFER IS NOT FAIR AND EQUITABLE BECAUSE THE BUYER IS VIOLATING THE DCF RULES. SPECIFICALLY, THE BUYER IS ADDING AND SUBTRACTING MONEY AT DIFFERENT POINTS IN TIME. THE WORTH OF THE DEAL RIGHT NOW IS $200 + $100/(1+0.05) = $295.24 THE WORTH OF THE DEAL 1 YEAR FROM NOW IS $200*(1+0.05) + $100 = $310.00 OR $295.24*(1+0.05) = $310.00 THE WORTH OF THE BUYER'S OFFER RIGHT NOW IS $300/(1+0.05) = $285.71 THE WORTH OF THE BUYER'S OFFER 1 YEAR FROM NOW IS $300.00

A B 1 PROBLEM 2.4 2 3 a FAIR AMOUNT NOW = $500 + $500/(1+0.06) = $971.70 4 5 b FAIR AMOUNT 1 YEAR FROM NOW = $500*(1+0.06) + $500 = $1030.00 6 OR $971.70*(1+0.06) = $1030.00

A B C D E 1 PROBLEM 2.5 2 3 CFD FROM BANK'S PERSPECTIVE 4 5 NOT NECESSARILY TO SCALE 6 7 (+) $X $X $X 8 9 10 0 1 2 3 11 12 13 (-) 14 15 $2,000

A B C D E F G H I J K L M N O 1 PROBLEM 2.6 2 3 CFD FROM YOUR PERSPECTIVE 4 5 NOT NECESSARILY TO SCALE 6 7 $10,000 8 9 10 11 12 13 $4,000 14 15 (+) 16 17 18 0 1 2 3 4 5 6 7 8 9 10 11 12 13 19 20 (-) 21 $2,880 $2,880 $2,880 $2,880 $2,880 22 $2,880 $2,880 $2,880 $2,880 $2,880

P 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

A B C D E F G 1 PROBLEM 2.7 2 3 FROM KAELYN'S GRANDFATHER'S PERSPECTIVE 4 5 NOT NECESSARILY TO SCALE 6 7 8 (+) 9 $2,000 10 11 0 1 2 3 4 5 12 13 (-) 14 15 16 17 18 19 20 21 22 23 24 25 26 $30,000

$X+6000 $X+4500 $X+3000 $X+1500 $X

A B C D E F G 1 PROBLEM 2.8 2 3 CFD FROM DAVID'S PERSPECTIVE 4 5 NOT NECESSARILY TO SCALE 6 7 $150,000 8 9 10 11 12 13 14 15 16 17 18 19 20 (+) 21 22 23 0 1 2 3 4 5 24 25 (-) $20,000 $20,000 26 27 28 29

$X $X+8000 $X+16,000 $X+24,000

L 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 $X+24,000 29

A B C D E 1 PROBLEM 2.9 2 3 CFD OF MERCRUISER CNC MACHINE 4 5 NOT NECESSARILY TO SCALE 6 7 (+) $7,000 $7,000 $7,000 8 9 10 0 1 2 3 11 $1,000 $1,000 $1,000 12 (-) 13 14 15 16 17 18 19 20 21 22 23 $50,000

$7,000

4 $1,000

6 $1,000

7 $1,000

8 $1,000

9 $1,000

10 $1,000

$1000+5000 SINCE PLANNING HORIZON IS 10 YEARS, WOULD NOT SHOW UPGRADE AT YEAR 10

A B C D E F G H I J K L M 1 PROBLEM 2.10 2 3 4 CFD OF APARTMENT RENT 5 6 NOT NECESSARILY TO SCALE 7 8 (+) 9 10 11 0 1 2 3 4 5 6 7 8 9 10 11 12 13 (-) 14 15 16 17 18 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150 $550+150 19 20 21 $550+450

$450

12 $150

O 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

A B C D E F G H I J 1 PROBLEM 2.11 2 3 USA DENIM (TWO MACHINES) 4 5 NOT NECESSARILY TO SCALE 6 7 0 1 2 3 4 5 6 7 8 8 9 (-) 10 11 12 13 $12,000 14 $14,000 15 $16,000 16 $18,000 17 $20,000 18 $22,000 19 20 21 22 $30,000 23 24 25 26 $38,000 27 28 29 30 31 32 33 34 35 36 $30,000+24,000

K 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

A B C D E 1 PROBLEM 2.12 2 3 LASER CUTTING MACHINE CFD 4 5 NOT NECESSARILY TO SCALE 6 7 $14,000 $14,000 $14,000 8 9 10 11 12 (+) 13 14 15 0 1 2 3 16 $2,000 17 (-) 18 19 20 21 22 23 24 25 26 27 $23,000

$14,000

$3,000

$4,000 $5,000

A B C D E F G H I J K L M 1 PROBLEM 2.13 2 3 CFD OF SYNTHETIC RUBBER BLENDING MACHINE 4 5 NOT NECESSARILY TO SCALE 6 $24,000-4000+8000-1600 7 $24,000-4000 $24,000-4000 $24,000-4000 8 $18,000-1600 $24,000-4000 $24,000-4000 $24,000-4000 9 $12,000-1200 10 $10,000-800 11 (+) 12 13 14 0 1 2 3 4 5 6 7 8 9 10 15 16 (-) 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 $62,000+8000

A 1 PROBLEM 2.14 2 3 4 5 6 7 a 8 9 b 10 11 12 13 14

i= n= F=

5.00% 12 $8,000

$5,000 USING SIMPLE INTEREST FORMULA THIS IS =8000/(1+0.05*12) P= $4,454.70 USING COMPOUND INTEREST FORMULA THIS IS =8000/(1+0.05)^12 P= $4,454.72 USING THE INTEREST TABLES THIS IS =$8,000*(P|F 5%,12) P= $4,454.70 USING EXCEL'S PV FUNCTION THIS IS =PV(5%,12,,-8000)

A B C D E F 1 PROBLEM 2.15 2 3 ACCT 4 5 1 i= 5.50% SIMPLE INTEREST 6 n= 5 7 P= $10,000.00 8 9 F= $12,750.00 USING SIMPLE INTEREST FORMULA THIS IS 10 =10000*(1+0.055*5) 11 12 2 i= 5.00% COMPOUNDED ANNUALLY 13 n= 5 14 P= $10,000.00 15 16 F= $12,762.82 USING COMPOUND INTEREST FORMULAS THIS IS 17 =10000*(1+0.05)^5 18 F= $12,762.80 USING THE INTEREST TABLES THIS IS 19 $10,000*(F|P 5%,5) 20 F= $12,762.82 USING EXCEL'S FV FUNCTION THIS IS 21 =FV(5%,5,,-10000) 22 23 3 i= 6.50% SIMPLE INTEREST 24 n= 5 25 P= $10,000.00 26 27 F= $13,250.00 USING SIMPLE INTEREST FORMULA THIS IS 28 =10000*(1+0.065*5) 29 30 4 i= 6.00% COMPOUNDED ANNUALLY 31 n= 5 32 P= $10,000.00 33 34 F= $13,382.26 USING COMPOUND INTEREST FORMULAS THIS IS 35 =10000*(1+0.06)^5 36 F= $13,382.30 USING THE INTEREST TABLES THIS IS 37 = $10,000*(F|P 6%,5) 38 F= $13,382.26 USING EXCEL'S FV FUNCTION THIS IS 39 =FV(6%,5,,-10000) 40 41 ACCOUNT 1 2 3 4 42 AMOUNT $12,750.00 $12,762.82 $13,250.00 $13,382.26 43 44 ACCOUNT 4 IS PREFERRED SINCE IT GIVES THE HIGHEST FUTURE VALUE

A 1 PROBLEM 2.16 2 3 a 4 5 6 7 8 9 10 11 12 13 b 14 15 16 17 18 19 20 21 22 23 24 25

i= n= P=

8.00% SIMPLE INTEREST 3 $1,000.00

$1,240.00 USING SIMPLE INTEREST FORMULA THIS IS =1000*(1+0.08*3)

TOTAL INTEREST

$240.00 THIS IS THE FUTURE VALUE OF $1,240 MINUS THE PRESENT VALUE OF $1,000

i= n= P=

8.00% COMPOUNDED ANNUALLY 3 $1,000.00

$1,259.71 USING COMPOUND INTEREST FORMULAS THIS IS =1000*(1+0.08)^3 $1,259.71 USING INTEREST TABLES THIS IS = $1,000*(F|P 8%,3) $1,259.71 USING EXCEL'S FV FUNCTION THIS IS =FV(8%,3,,-1000)

F= F=

TOTAL INTEREST

$259.71 THIS IS THE FUTURE VALUE OF $1,259.71 MINUS THE PRESENT VALUE OF $1,000.

A 1 PROBLEM 2.17 2 3 a 4 5 6 7 8 9 10 b 11 12 13 14 15 16 17 18 19

i= 12.00% SIMPLE INTEREST n= 5 P= $3,000.00 F= $4,800.00 USING SIMPLE INTEREST FORMULA THIS IS =3000*(1+.012*5) i= 12.00% COMPOUNDED ANNUALLY n= 5 P= $3,000.00 F= $5,287.03 USING COMPOUND INTEREST FORMULAS THIS IS =3000*(1+0.12)^5 F= $5,287.02 USING INTEREST TABLES THIS IS =$3,000*(F|P 12%,5) F= $5,287.03 USING EXCEL'S FV FUNCTION THIS IS =FV(12%,5,,-3000)

A 1 PROBLEM 2.18 2 3 a 4 5 6 7 8 9 10 b 11 12 c 13 14 15 16 17 18 19 20 21 22 23 d 24

i= n= P=

5.00% 3 $1,000.00

$1,150.00 USING SIMPLE INTEREST FORMULA THIS IS =1000*(1+0.05*3)

TOTAL INTEREST

$150.00

i= n= P=

5.00% 3 $1,000.00

$1,157.63 USING COMPOUND INTEREST FORMULAS THIS IS =1000*(1+0.05)^3 $1,157.63 USING INTEREST TABLES THIS IS =$1,000*(F|P 5%,3) $1,157.63 USING EXCEL'S FV FUNCTION THIS IS =FV(5%,3,,-1000)

F= F=

TOTAL INTEREST

$157.63 THIS IS THE FUTURE VALUE OF $1,157.63 MINUS THE PRESENT VALUE OF $1,000.

A B C D E F G 1 PROBLEM 2.19 2 3 UNCLE ESWAR 4 i= 8.00% COMPOUNDED ANNUALLY 5 n= 5 6 P= $5,000.00 7 8 F= $7,346.64 USING COMPOUND INTEREST FORMULAS THIS IS 9 =5000*(1+0.08)^5 10 F= $7,346.65 USING INTEREST TABLES THIS IS 11 =$5,000*(F|P 8%,5) 12 F= $7,346.64 USING EXCEL'S FV FUNCTION THIS IS 13 =FV(8%,5,,-5000) 14 15 UNCLE SHANKAR 16 i= 9.00% SIMPLE INTEREST 17 n= 5 18 P= $5,000.00 19 20 F= $7,250.00 USING SIMPLE INTEREST FORMULA THIS IS 21 =5000*(1+0.09*5) 22 23 GO WITH UNCLE SHANKAR'S LOAN

A 1 PROBLEM 2.20 2 3 a 4 5 6 7 8 9 10 11 12 13 14 b 15 16 17 18 19 20 21 22 23 24 25

i= 8.00% n= 10 F= $8,000.00 P= $3,705.55 USING COMPOUND INTEREST FORMULAS THIS IS =8000/(1+0.08)^10 P= $3,705.52 USING INTEREST TABLES THIS IS =$8,000*(P|F 8%,10) P= $3,705.55 USING EXCEL'S PV FUNCTION THIS IS =PV(8%,10,,-8000) i=

11.59% USING SIMPLE INTEREST FORMULA THIS IS =(8000-3705.52)/(3705.52*10) OR, CAN USE SOLVER TO FIND VALUE OF i

i= 11.59% <--SOLVER CHANGED CELL n= 10 F= $8,000.00 P= $3,705.55 <--SOLVER TARGET CELL USING SIMPLE INTEREST FORMULA THIS IS =8000/(1+i*10)

A 1 PROBLEM 2.21 2 3 a 4 5 6 7 8 9 10 11 12 13 14 b 15 16 17 18 19 20 21 22 23 24 25

i= 6.00% n= 4 P= $12,000.00 F= $15,149.72 USING COMPOUND INTEREST FORMULAS THIS IS =12000*(1+0.06)^4 F= $15,149.76 USING INTEREST TABLES THIS IS =$12,000*(F|P 6%,4) F= $15,149.72 USING EXCEL'S FV FUNCTION THIS IS =FV(6%,4,,-12000) i=

6.56% USING SIMPLE INTEREST FORMULA THIS IS =(15149.72-12000)/(12000*4) OR, CAN USE SOLVER TO FIND VALUE OF i

i= 6.56% <--SOLVER CHANGED CELL n= 4 P= $12,000.00 F= $15,149.72 <--SOLVER TARGET CELL USING SIMPLE INTEREST FORMULA THIS IS =12000*(1+i*4)

A 1 PROBLEM 2.22 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

i= n= P=

7.00% 5 $11,000.00

$15,428.07 USING COMPOUND INTEREST FORMULAS THIS IS =11000*(1+0.07)^5 $15,428.08 USING INTEREST TABLES THIS IS =$11,000*(F|P 7%,5) $15,428.07 USING EXCEL'S FV FUNCTION THIS IS =FV(7%,5,,-11000)

F= F=

PRINCIPAL $11,000.00 FINAL AMT $15,428.07 INTEREST $4,428.07 =15428.07-11000.00

A B C D E F G H 1 PROBLEM 2.23 2 3 i= 8.00% 4 n= 4 5 P= $2,500.00 6 7 AT THE END OF 4 YEARS AT 8% SIMPLE INTEREST THE MAN HAS: 8 F= $3,300.00 USING SIMPLE INTEREST FORMULA THIS IS 9 =2500*(1+0.08*4) 10 11 NOW, REINVESTING THE $3,300.00 FOR 9 YEARS RESULTS IN 12 i= 6.00% 13 n= 9 14 P= $3,300.00 15 16 AT THE END OF 9 MORE YEARS AT 6% COMPOUND INTEREST THE MAN HAS: 17 F= $5,575.28 USING COMPOUND INTEREST FORMULAS THIS IS 18 =3300*(1+0.06)^9 19 F= $5,575.28 USING INTEREST TABLES THIS IS 20 =$3,300*(F|P 6%,9) 21 F= $5,575.28 USING EXCEL'S FV FUNCTION THIS IS 22 =FV(6%,9,,-3300)

A B C D E F G H 1 PROBLEM 2.24 2 3 ACCOUNT 4 1 i= 7.00% 5 n= 4 6 P= $10,000.00 7 8 F= $13,107.96 USING COMPOUND INTEREST FORMULAS THIS IS 9 =10000*(1+0.07)^4 10 F= $13,108.00 USING INTEREST 10,000*(F|P TABLES 7%,4) THIS IS 11 =$10,000*(F|P 7%,4) 12 F= $13,107.96 USING EXCEL'S FV FUNCTION THIS IS 13 =FV(7%,4,,-10000) 14 15 2 i= 7.50% 16 n= 4 17 P= $10,000.00 18 19 F= $13,000.00 USING SIMPLE INTEREST FORMULA THIS IS 20 =10000*(1+0.075*4) 21 22 3 i= 7.50% 23 n= 4 24 P= $10,000.00 25 26 F= $13,354.69 USING COMPOUND INTEREST FORMULAS THIS IS 27 $13,354.69 28 F= $13,354.70 USING INTEREST TABLES (USER TAB) THIS IS 29 =$10,000*(F|P 7.5%,4) 30 F= $13,354.69 USING EXCEL'S FV FUNCTION THIS IS 31 =FV(7.5%,4,,-10000) 32 33 4 i= 8.25% 34 n= 4 35 P= $10,000.00 36 37 F= $13,300.00 USING SIMPLE INTEREST FORMULA THIS IS 38 =10000*(1+0.0825*4) 39 40 ACCOUNT 1 2 3 4 41 AMOUNT OWED $13,107.96 $13,000.00 $13,354.69 $13,300.00 42 PREFER LOAN 2

A B C D E F G H 1 PROBLEM 2.25 2 3 F|P 4 5 i= 8.00% 6 n= 3 7 (F|P i%,n) = 1.25971 USING COMPOUND INTEREST FORMULAS THIS IS 8 =(1+0.08)^3 9 10 P|F 11 12 i= 10.00% 13 n= 20 14 (P|F i%,n) = 0.14864 USING COMPOUND INTEREST FORMULAS THIS IS 15 =1/(1+0.1)^20 16 17 CHECKS OK WITH APPENDIX A

A 1 PROBLEM 2.26 2 3 4 5 6 7 8 9 10 11 12

i= n= P=

8.00% 5 $25,000.00

$36,733.20 USING COMPOUND INTEREST FORMULAS THIS IS =25000*(1+0.08)^5 $36,733.25 USING INTEREST TABLES THIS IS =$25,000*(F|P 8%,5) $36,733.20 USING EXCEL'S FV FUNCTION THIS IS =FV(8%,5,,-25000)

F= F=

A 1 PROBLEM 2.27 2 3 4 5 6 7 8 9 10 11 12

i= 4.00% n= 10 F= $100,000.00 P= P= P=

$67,556.42 USING COMPOUND INTEREST FORMULAS THIS IS =100000/(1+0.04)^10 $67,556.00 USING INTEREST TABLES THIS IS =$100,000*(P|F 4%,10) $67,556.42 USING EXCEL'S PV FUNCTION THIS IS =PV(4%,10,,-100000)

A 1 PROBLEM 2.28 2 3 4 5 6 7 8 9 10 11 12

i= 7.00% n= 10 P= $25,000.00 F= $49,178.78 USING COMPOUND INTEREST FORMULAS THIS IS =25000*(1+0.07)^10 F= $49,178.75 USING INTEREST TABLES THIS IS =$25,000*(F|P 7%,10) F= $49,178.78 USING EXCEL'S FV FUNCTION THIS IS =FV(7%,10,,-25000)

A 1 PROBLEM 2.29 2 3 4 5 6 7 8 9 10 11 12

i= 5.00% n= 25 F= $150,000.00 P= P= P=

$44,295.42 USING COMPOUND INTEREST FORMULAS THIS IS =150000/(1+0.05)^25 $44,295.00 USING INTEREST TABLES THIS IS =$150,000*(P|F 5%,25) $44,295.42 USING EXCEL'S PV FUNCTION THIS IS =PV(5%,25,,-150000)

A 1 PROBLEM 2.30 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

P= n= F=

$0.04 49 $0.41

USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^n SOLVING FOR i i=(F/P)^(1/n)-1 4.8641% =(0.41/0.04)^(1/49)-1

OR, CAN USE RATE FUNCTION P= $0.04 n= 49 F= $0.41 i= 4.8641% =RATE(49,,-0.04,0.41)

OR, CAN USE SOLVER P= $0.04 n= 49 i= 4.8641% <--SOLVER CHANGED CELL F=

$0.41 <--SOLVER TARGET CELL USING COMPOUND INTEREST FORMULAS THIS IS =$0.04*(1+i)^49

$0.41 COULD HAVE USED THIS AS SOLVER TARGET CELL USING EXCEL'S FV FUNCTION THIS IS =FV(i%,49,,-0.04)

A B 1 PROBLEM 2.31 2 3 a i= 4 n= 5 P= 6 7 F= 8 9 F= 10 11 F= 12 13 14 b i= 15 n= 16 P= 17 18 F= 19 20 F= 21 22 F= 23 24 25 c i= 26 n= 27 P= 28 29 F= 30 31 F= 32 33 F= 34 35 36 d i= 37 n= 38 P= 39 40 F= 41 42 F= 43 44 F= 45

8.00% COMPOUNDED ANNUALLY 10 $1,000.00 $2,158.92 USING COMPOUND INTEREST FORMULAS THIS IS =1000*(1+0.08)^10 $2,158.92 USING INTEREST TABLES THIS IS $1,000*(F|P 8%,10) $2,158.92 USING EXCEL'S FV FUNCTION THIS IS =FV(8%,10,,-1000) 11.00% 4 $5,000.00 $7,590.35 USING COMPOUND INTEREST FORMULAS THIS IS =5000*(1+0.11)^4 $7,590.35 USING INTEREST TABLES THIS IS $5,000*(F|P 11%,4) $7,590.35 USING EXCEL'S FV FUNCTION THIS IS =FV(11%,4,,-5000) 9.00% COMPOUNDED ANNUALLY 7 $13,000.00 $23,764.51 USING COMPOUND INTEREST FORMULAS THIS IS =13000*(1+0.09)^7 $23,764.52 USING INTEREST TABLES THIS IS $13,000*(F|P 9%,7) $23,764.51 USING EXCEL'S FV FUNCTION THIS IS =FV(9%,7,,-13000) 10.00% COMPOUNDED ANNUALLY 3 $25,000.00 $33,275.00 USING COMPOUND INTEREST FORMULAS THIS IS =25000*(1+0.1)^3 $33,275.00 USING INTEREST TABLES THIS IS $25,000*(F|P 10%,3) $33,275.00 USING EXCEL'S FV FUNCTION THIS IS =FV(10%,3,,-25000)

A 1 PROBLEM 2.32 2 3 a 4 5 6 7 8 9 10 11 12 13 14 b 15 16 17 18 19 20 21 22 23 24 25 c 26 27 28 29 30 31 32 33 34 35 36 d 37 38 39 40 41 42 43 44 45

i= 5.00% n= 6 F= $10,000.00 P= P= P=

$7,462.15 USING COMPOUND INTEREST FORMULAS THIS IS =10000/(1+0.05)^6 $7,462.20 USING INTEREST TABLES THIS IS =$10,000*(P|F 5%,6) $7,462.15 USING EXCEL'S PV FUNCTION THIS IS =PV(5%,6,,-10000)

i= n= F=

8.00% 4 $6,500.00

$4,777.69 USING COMPOUND INTEREST FORMULAS THIS IS =6500/(1+0.08)^4 $4,777.70 USING INTEREST TABLES THIS IS =$6,500*(P|F 8%,4) $4,777.69 USING EXCEL'S PV FUNCTION THIS IS =PV(8%,4,,-6500)

P= P=

i= n= F=

6.00% 12 $3,400.00

$1,689.70 USING COMPOUND INTEREST FORMULAS THIS IS =3400/(1+0.06)^12 $1,689.70 USING INTEREST TABLES THIS IS =$3,400*(P|F 6%,12) $1,689.70 USING EXCEL'S PV FUNCTION THIS IS =PV(6%,12,,-3400)

P= P=

i= 10.00% n= 5 F= $13,500.00 P= P= P=

$8,382.44 USING COMPOUND INTEREST FORMULAS THIS IS =13500/(1+0.1)^5 $8,382.42 USING INTEREST TABLES THIS IS =$13,500*(P|F 10%,5) $8,382.44 USING EXCEL'S PV FUNCTION THIS IS =PV(10%,5,,-13500)

A 1 PROBLEM 2.33 2 3 a 4 5 6 7 8 9 10 11 12 13 14 b 15 16 17 18 19 20 21 22 23 24 25 c 26 27 28 29 30 31 32 33 34 35 36 d 37 38 39 40 41 42 43 44 45 46 47 e 48 49 50 51 52 53 54 55 56

i= n= P=

14.00% COMPOUNDED ANNUALLY 7 $3,000.00

$7,506.81 USING COMPOUND INTEREST FORMULAS THIS IS =3000*(1+0.14)^7 $7,506.81 USING ELECTRONIC INTEREST TABLES THIS IS =$3,000*(F|P 14%,7) $7,506.81 USING EXCEL'S FV FUNCTION THIS IS =FV(14%,7,,-3000)

F= F=

i= n= P= F= F= F=

i= n= P=

12.00% 17 $1,600.00 $10,985.67 USING COMPOUND INTEREST FORMULAS THIS IS =1600*(1+0.12)^17 $10,985.66 USING INTEREST TABLES THIS IS =$1,600*(F|P 12%,17) $10,985.67 USING EXCEL'S FV FUNCTION THIS IS =FV(12%,17,,-1600) 16.00% COMPOUNDED ANNUALLY 38 $20,000.00

F= $5,629,030.30 USING COMPOUND INTEREST FORMULAS THIS IS =20000*(1+0.16)^38 F= $5,629,030.20 USING ELECTRONIC INTEREST TABLES THIS IS =$20,000*(F|P 16%,38) F= $5,629,030.30 USING EXCEL'S FV FUNCTION THIS IS =FV(16%,38,,-20000) i= n= P= F= F= F=

i= n= P= F= F= F=

8.00% COMPOUNDED ANNUALLY 71 $3,500.00 $826,332.21 USING COMPOUND INTEREST FORMULAS THIS IS =3500*(1+0.08)^71 $826,332.22 USING ELECTRONIC INTEREST TABLES THIS IS =$3,500*(F|P 8%,71) $826,332.21 USING EXCEL'S FV FUNCTION THIS IS =FV(8%,71,,-3500) 11.50% COMPOUNDED ANNUALLY 34 $5,000.00 $202,448.93 USING COMPOUND INTEREST FORMULAS THIS IS =5000*(1+0.115)^34 $202,448.95 USING ELECTRONIC INTEREST TABLES THIS IS =$5,000*(F|P 11.5%,34) $202,448.93 USING EXCEL'S FV FUNCTION THIS IS =FV(11.5%,34,,-5000)

A 1 PROBLEM 2.34 2 3 a 4 5 6 7 8 9 10 11 12 13 14 b 15 16 17 18 19 20 21 22 23 24 25 c 26 27 28 29 30 31 32 33 34 35 36 d 37 38 39 40 41 42 43 44 45 46 47 e 48 49 50 51 52 53 54 55 56

i= 9.00% n= 5 F= $19,000.00 P= $12,348.70 USING COMPOUND INTEREST FORMULAS THIS IS =19000/(1+0.09)^5 P= $12,348.67 USING INTEREST TABLES THIS IS =$19,000*(P|F 9%,5) P= $12,348.70 USING EXCEL'S PV FUNCTION THIS IS =PV(9%,5,,-19000) i= n= F=

15.00% 12 $8,300.00

$1,551.33 USING COMPOUND INTEREST FORMULAS THIS IS =8300/(1+0.15)^12 $1,551.35 USING INTEREST TABLES THIS IS =$8,300*(P|F 15%,12) $1,551.33 USING EXCEL'S PV FUNCTION THIS IS =PV(15%,12,,-8300)

P= P=

i= n= F= P= P= P=

12.00% 53 $6,200.00 $15.27 USING COMPOUND INTEREST FORMULAS THIS IS =6200/(1+0.12)^53 $15.27 USING ELECTRONIC INTEREST TABLES THIS IS =$6,200*(P|F 12%,53) $15.27 USING EXCEL'S PV FUNCTION THIS IS =PV(12%,53,,-6200)

i= 19.20% n= 18 F= $13,000.00 P= P= P=

$550.77 USING COMPOUND INTEREST FORMULAS THIS IS =13000/(1+0.192)^18 $550.77 USING ELECTRONIC INTEREST TABLES THIS IS =$13,000*(P|F 19.2%,18) $550.77 USING EXCEL'S PV FUNCTION THIS IS =PV(19.2%,18,,-13000)

i= n= F=

8.00% 10 $5,000.00

$2,315.97 USING COMPOUND INTEREST FORMULAS THIS IS =5000/(1+0.08)^10 $2,315.95 USING INTEREST TABLES THIS IS =$5,000*(P|F 8%,10) $2,315.97 USING EXCEL'S PV FUNCTION THIS IS =PV(8%,10,,-5000)

P= P=

A B C D E F 1 PROBLEM 2.35 2 3 a P= $10,000.00 4 n= 10 5 F= $23,674.00 6 7 USING COMPOUND INTEREST FORMULAS THIS IS 8 F=P*(1+i)^n 9 SOLVING FOR i 10 i=(F/P)^(1/n)-1 11 i= 9.0002% =(23674/10000)^(1/10)-1 12 13 14 OR, CAN USE RATE FUNCTION 15 P= $10,000.00 16 n= 10 17 F= $23,674.00 18 19 i= 9.0002% =RATE(10,,-10000,23674) 20 21 22 OR, CAN USE SOLVER 23 P= $10,000.00 24 n= 10 25 26 i= 9.0002% <--SOLVER CHANGED CELL 27 28 F= $23,674.00 <--SOLVER TARGET CELL 29 USING COMPOUND INTEREST FORMULAS THIS IS 30 =$10,000*(1+i)^10 31 32 F= $23,674.00 COULD HAVE USED THIS AS SOLVER TARGET CELL 33 USING EXCEL'S FV FUNCTION THIS IS 34 =FV(i%,10,,-10000) 35 36 b P= $2,000.00 37 n= 18 38 F= $15,380.00 39 40 USING COMPOUND INTEREST FORMULAS THIS IS 41 F=P*(1+i)^n 42 SOLVING FOR i 43 i=(F/P)^(1/n)-1 44 i= 12.0000% =(15380/2000)^(1/18)-1 45 46 47 OR, CAN USE RATE FUNCTION 48 P= $2,000.00 49 n= 18 50 F= $15,380.00 51 52 i= 12.0000% =RATE(18,,-2000,15380) 53 54 55 OR, CAN USE SOLVER 56 P= $2,000.00 57 n= 18

A 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

12.0000% <--SOLVER CHANGED CELL

$15,380.00 <--SOLVER TARGET CELL USING COMPOUND INTEREST FORMULAS THIS IS =$2000*(1+i)^18

$15,380.00 COULD HAVE USED THIS AS SOLVER TARGET CELL USING EXCEL'S FV FUNCTION THIS IS =FV(i%,18,,-2000)

P= n= F=

$2,500.00 5 $4,212.00 USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^n SOLVING FOR i i=(F/P)^(1/n)-1 10.9966% =(4212/2500)^(1/5)-1

OR, CAN USE RATE FUNCTION P= $2,500.00 n= 5 F= $4,212.00 i=

10.9966% =RATE(5,,-2500,4212)

OR, CAN USE SOLVER P= $2,500.00 n= 5 i=

10.9966% <--SOLVER CHANGED CELL

$4,212.00 <--SOLVER TARGET CELL USING COMPOUND INTEREST FORMULAS THIS IS =$2500*(1+i)^5

$4,212.00 COULD HAVE USED THIS AS SOLVER TARGET CELL USING EXCEL'S FV FUNCTION THIS IS =FV(i%,5,,2500)

A 1 PROBLEM 2.36 2 3 4 5 6 7 a 8 9 b 10 11 c 12

i= 11.00% n= 9 F= $15,000.00 P= P= P=

$5,863.80 USING INTEREST TABLES THIS IS =$15,000*(P|F 11%,9) $5,863.87 USING COMPOUND INTEREST FORMULAS THIS IS =15000/(1+0.11)^9 $5,863.87 USING EXCEL'S PV FUNCTION THIS IS =PV(11%,9,,-15000)

A 1 PROBLEM 2.37 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

FOR EACH OF THE 3 CHOICES, DETERMINE THE VALUE AT THE SAME POINT IN TIME. BELOW, THE POINT IN TIME WILL BE THE PRESENT (TIME 0) i=

8.00%

CHOICE 1: TAKE TODAY P= $1,000.00 ALREADY AT TIME 0 CHOICE 2: WAIT 3 YEARS AND TAKE F= $1,500.00 n= 3 P= $1,190.75 USING COMPOUND INTEREST FORMULAS THIS IS =1500/(1+0.08)^3 P= $1,190.75 USING INTEREST TABLES THIS IS =$1,500*(P|F 8%,3) P= $1,190.75 USING EXCEL'S PV FUNCTION THIS IS =PV(8%,3,,-1500) CHOICE 3: WAIT 5 YEARS AND TAKE F= 3000 n= 5 P= $2,041.75 USING COMPOUND INTEREST FORMULAS THIS IS =3000/(1+0.08)^5 P= $2,041.74 USING INTEREST TABLES THIS IS =$3,000*(P|F 8%,5) P= $2,041.75 USING EXCEL'S PV FUNCTION THIS IS =PV(8%,5,,-3000) THE HIGHEST PRESENT VALUE IS ACHIEVED BY TAKING THE $3,000 AFTER 5 YEARS

A B C D E F G H 1 PROBLEM 2.38 2 3 i= 10.00% 4 n= 7 5 F= $23,384.61 6 7 TO FIND HOW MUCH HE BORROWED, FIND THE PW OF THE LOAN PAYOFF 8 9 P= $12,000.00 USING COMPOUND INTEREST FORMULAS THIS IS 10 =23384.61/(1+0.1)^7 11 P= $12,000.05 USING INTEREST TABLES THIS IS 12 =$23,384.61*(P|F 10%,7) 13 P= $12,000.00 USING EXCEL'S PV FUNCTION THIS IS 14 =PV(10%,7,,-23384.61)

A B C D E F G H 1 PROBLEM 2.39 2 3 i= 11.50% 4 n= 37 5 SET THE FUTURE WORTH AT $1.00 6 F= $1.00 7 8 THE (P|F 11.5%,37) FACTOR IS 9 10 P= 0.0178168 USING COMPOUND INTEREST FORMULAS THIS IS 11 =1/(1+0.115)^37 12 P= 0.0178168 USING EXCEL'S PV FUNCTION THIS IS 13 =PV(11.5%,37,,-1) 14 15 BOTH RESULTS ARE IDENTICAL

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

A PROBLEM 2.40

i= 12.00% n= 7 F= $6,000.00 TO FIND THE SINGLE SUM OF MONEY DEPOSITED TODAY, FIND THE PW OF THE WITHDRAWAL a

P= $2,714.10 USING INTEREST TABLES THIS IS =$6,000*(P|F 12%,7)

P= $2,714.10 USING COMPOUND INTEREST FORMULAS THIS IS =6000/(1+0.12)^7

P= $2,714.10 USING EXCEL'S PV FUNCTION THIS IS =PV(12%,7,,-6000)

A 1 PROBLEM 2.41 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

P= n= F=

$5,000.00 10 $8,955.00

USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^n SOLVING FOR i i=(F/P)^(1/n)-1 6.0009% =(8955/5000)^(1/10)-1

OR, CAN USE RATE FUNCTION P= $5,000.00 n= 10 F= $8,955.00 i=

6.0009% =RATE(10,,-5000,8955)

OR, CAN USE SOLVER P= $5,000.00 n= 10 i=

6.0009% <--SOLVER CHANGED CELL

$8,955.00 <--SOLVER TARGET CELL USING COMPOUND INTEREST FORMULAS THIS IS =$5,000*(1+i)^10

$8,955.00 COULD HAVE USED THIS AS SOLVER TARGET CELL USING EXCEL'S FV FUNCTION THIS IS =FV(i%,10,,-5000)

A 1 PROBLEM 2.42 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

P= n= F=

$1,500.00 3 $2,500.00

USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^n SOLVING FOR i i=(F/P)^(1/n)-1 18.5631% =(2500/1500)^(1/3)-1

OR, CAN USE RATE FUNCTION P= $1,500.00 n= 3 F= $2,500.00 i=

18.5631% =RATE(3,,-1500,2500)

OR, CAN USE SOLVER P= $1,500.00 n= 3 i=

18.5631% <--SOLVER CHANGED CELL

F= $2,500.00 <--SOLVER TARGET CELL USING COMPOUND INTEREST FORMULAS THIS IS =$1,500*(1+i)^3 F= $2,500.00 COULD HAVE USED THIS AS SOLVER TARGET CELL USING EXCEL'S FV FUNCTION THIS IS =FV(i%,3,,-1500)

A 1 PROBLEM 2.43 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37

P= i= F=

$2,500.00 5.00% $4,430.00

USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^n SOLVING FOR n n=ln(F/P)/ln(1+i) n= 11.73 =LN(4430/2500)/LN(1+0.05) USE 12 YEARS

OR, CAN USE NPER EXCEL FUNCTION P= $2,500.00 i= 5.00% F= $4,430.00 n=

11.73 =NPER(5%,,-2500,4430) USE 12 YEARS

OR, CAN USE SOLVER P= $2,500.00 i= 5.00% n=

11.73 <--SOLVER CHANGED CELL USE 12 YEARS

F= $4,430.00 <--SOLVER TARGET CELL USING COMPOUND INTEREST FORMULAS THIS IS =$2,500*(1+0.05)^n F= $4,430.00 COULD HAVE USED THIS AS SOLVER TARGET CELL USING EXCEL'S FV FUNCTION THIS IS =FV(5%,n,,-2500)

A B C D E 1 PROBLEM 2.44 2 3 a P= $1.00 4 n= 10 5 F= $2.00 6 7 USING COMPOUND INTEREST FORMULAS THIS IS 8 F=P*(1+i)^n 9 SOLVING FOR i 10 i=(F/P)^(1/n)-1 11 i= 7.1773% =(2/1)^(1/10)-1 12 13 14 OR, CAN USE RATE FUNCTION 15 P= $1.00 16 n= 10 17 F= $2.00 18 19 i= 7.1773% =RATE(10,,-1.00,2.00) 20 21 22 b P= $1.00 23 n= 10 24 F= $3.00 25 26 USING COMPOUND INTEREST FORMULAS THIS IS 27 F=P*(1+i)^n 28 SOLVING FOR i 29 i=(F/P)^(1/n)-1 30 i= 11.6123% =(3/1)^(1/10)-1 31 32 33 OR, CAN USE RATE FUNCTION 34 P= $1.00 35 n= 10 36 F= $3.00 37 38 i= 11.6123% =RATE(10,,-1.00,3.00) 39 40 41 c P= $1.00 42 n= 10 43 F= $4.00 44 45 USING COMPOUND INTEREST FORMULAS THIS IS 46 F=P*(1+i)^n 47 SOLVING FOR i 48 i=(F/P)^(1/n)-1 49 i= 14.8698% =(4/1)^(1/10)-1 50 51 52 OR, CAN USE RATE FUNCTION 53 P= $1.00 54 n= 10 55 F= $4.00 56 57 i= 14.8698% =RATE(10,,-1,4)

A B C D E F 1 PROBLEM 2.45 2 3 P= $1.00 4 i= 9.00% 5 F= $2.00 6 7 USING COMPOUND INTEREST FORMULAS THIS IS 8 F=P*(1+i)^n 9 SOLVING FOR n 10 n=ln(F/P)/ln(1+i) 11 n= 8.04 =LN(2/1)/LN(1+0.09) 12 USE 9 YEARS 13 14 15 OR, CAN USE NPER EXCEL FUNCTION 16 P= $1.00 17 i= 9.00% 18 F= $2.00 19 20 n= 8.04 =NPER(5%,,-2500,4430) 21 USE 9 YEARS 22 23 24 OR, CAN USE SOLVER 25 P= $1.00 26 i= 9.00% 27 28 n= 8.04 <--SOLVER CHANGED CELL 29 USE 9 YEARS 30 31 F= $2.00 <--SOLVER TARGET CELL 32 USING COMPOUND INTEREST FORMULAS THIS IS 33 =$2,500*(1+0.05)^n 34 35 F= $2.00 COULD HAVE USED THIS AS SOLVER TARGET CELL 36 USING EXCEL'S FV FUNCTION THIS IS 37 =FV(5%,n,,-2500)

A B C D E F 1 PROBLEM 2.46 2 3 P= $1.00 4 i= 6.00% 5 F= $3.00 6 7 USING COMPOUND INTEREST FORMULAS THIS IS 8 F=P*(1+i)^n 9 SOLVING FOR n 10 n=ln(F/P)/ln(1+i) 11 n= 18.85 =LN(3/1)/LN(1+0.06) 12 USE 19 YEARS 13 14 15 OR, CAN USE NPER EXCEL FUNCTION 16 P= $1.00 17 i= 6.00% 18 F= $3.00 19 20 n= 18.85 =NPER(6%,,-1.00,3.00) 21 USE 19 YEARS 22 23 24 OR, CAN USE SOLVER 25 P= $1.00 26 i= 6.00% 27 28 n= 18.85 <--SOLVER CHANGED CELL 29 USE 19 YEARS 30 31 F= $3.00 <--SOLVER TARGET CELL 32 USING COMPOUND INTEREST FORMULAS THIS IS 33 =$1.00*(1+0.06)^n 34 35 F= $3.00 COULD HAVE USED THIS AS SOLVER TARGET CELL 36 USING EXCEL'S FV FUNCTION THIS IS 37 =FV(6%,n,,-1.00)

A 1 PROBLEM 2.47 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38

P= n= F=

$1.00 10 $3.00

USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^n SOLVING FOR i i=(F/P)^(1/n)-1 i=

11.6123% =(3/1)^(1/10)-1 USE 12%

OR, CAN USE RATE FUNCTION P= $1.00 n= 10 F= $3.00 i=

11.6123% =RATE(10,,-1,3) USE 12%

OR, CAN USE SOLVER P= $1.00 n= 10 i= 11.6123% <--SOLVER CHANGED CELL USE 12% F=

$3.00 <--SOLVER TARGET CELL USING COMPOUND INTEREST FORMULAS THIS IS =$1.00*(1+i)^10

$3.00 COULD HAVE USED THIS AS SOLVER TARGET CELL USING EXCEL'S FV FUNCTION THIS IS =FV(i%,10,,-1)

A B C D E 1 PROBLEM 2.48 2 3 a P= $1.00 4 i= 6.00% 5 F= $2.00 6 7 USING COMPOUND INTEREST FORMULAS THIS IS 8 F=P*(1+i)^n 9 SOLVING FOR n 10 n=ln(F/P)/ln(1+i) 11 n= 11.90 =LN(2/1)/LN(1+0.06) 12 USE 12 YEARS 13 14 15 OR, CAN USE NPER EXCEL FUNCTION 16 P= $1.00 17 i= 6.00% 18 F= $2.00 19 20 n= 11.90 =NPER(6%,,-1.00,2.00) 21 USE 12 YEARS 22 23 24 OR, CAN USE SOLVER 25 P= $1.00 26 i= 6.00% 27 28 n= 11.90 <--SOLVER CHANGED CELL 29 USE 12 YEARS 30 31 F= $2.00 <--SOLVER TARGET CELL 32 USING COMPOUND INTEREST FORMULAS THIS IS 33 =$1.00*(1+0.06)^n 34 35 F= $2.00 COULD HAVE USED THIS AS SOLVER TARGET CELL 36 USING EXCEL'S FV FUNCTION THIS IS 37 =FV(6%,n,,-1.00) 38 39 40 b P= $1.00 41 i= 6.00% 42 F= $3.00 43 44 USING COMPOUND INTEREST FORMULAS THIS IS 45 F=P*(1+i)^n 46 SOLVING FOR n 47 n=ln(F/P)/ln(1+i) 48 n= 18.85 =LN(3/1)/LN(1+0.06) 49 USE 19 YEARS 50 51 52 OR, CAN USE NPER EXCEL FUNCTION 53 P= $1.00 54 i= 6.00% 55 F= $3.00 56 57 n= 18.85 =NPER(6%,,-1.00,3.00)

A 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111

C USE 19 YEARS

OR, CAN USE SOLVER P= $1.00 i= 6.00% n=

18.85 <--SOLVER CHANGED CELL USE 19 YEARS

F= $3.00 <--SOLVER TARGET CELL USING COMPOUND INTEREST FORMULAS THIS IS =$1.00*(1+0.06)^n F= $3.00 COULD HAVE USED THIS AS SOLVER TARGET CELL USING EXCEL'S FV FUNCTION THIS IS =FV(6%,n,,-1.00)

P= $1.00 i= 6.00% F= $4.00 USING COMPOUND INTEREST FORMULAS THIS IS F=P*(1+i)^n SOLVING FOR n n=ln(F/P)/ln(1+i) n= 23.79 =LN(4/1)/LN(1+0.06) USE 24 YEARS

OR, CAN USE NPER EXCEL FUNCTION P= $1.00 i= 6.00% F= $4.00 n=

23.79 =NPER(6%,,-1.00,4.00) USE 24 YEARS

OR, CAN USE SOLVER P= $1.00 i= 6.00% n=

23.79 <--SOLVER CHANGED CELL USE 24 YEARS

F= $4.00 <--SOLVER TARGET CELL USING COMPOUND INTEREST FORMULAS THIS IS =$1.00*(1+0.06)^n F= $4.00 COULD HAVE USED THIS AS SOLVER TARGET CELL USING EXCEL'S FV FUNCTION THIS IS =FV(6%,n,,-1.00)

A B C D E F G H 1 PROBLEM 2.49 2 3 a i= 5.00% 4 5 APPR 1 APPR 2 APPR 3 6 14.40000 F|P 5%,14 1.97993 14.20670 7 =72/(100*0.05) F|P 5%,15 2.07893 =LOG(2)/LOG(1+0.05) 8 INTERPOLATING 14.20273 9 =14+(2-1.97993)/(2.07893-1.97993) 10 11 APPR 4 APPR 5 12 14.20670 n= 14.20670 <--SOLVER CHANGED CELL 13 =NPER(5%,,-1,2) F= $2.00 <--SOLVER TARGET CELL 14 =FV(5%,n,,-1) 15 16 APPR 6 17 n= 14.20658 <--GOAL SEEK CHANGED CELL 18 F= $2.00 <--GOAL SEEK SET CELL 19 =FV(5%,n,,-1) 20 21 22 b i= 7.00% 23 24 APPR 1 APPR 2 APPR 3 25 10.28571 F|P 7%,10 1.96715 10.24477 26 =72/(100*0.07) F|P 7%,11 2.10485 =LOG(2)/LOG(1+0.07) 27 INTERPOLATING 10.23856 28 =10+(2-1.96715)/(2.10485-1.96715) 29 30 APPR 4 APPR 5 31 10.24477 n= 10.24477 <--SOLVER CHANGED CELL 32 =NPER(7%,,-1,2) F= $2.00 <--SOLVER TARGET CELL 33 =FV(7%,n,,-1) 34 35 APPR 6 36 n= 10.24499 <--GOAL SEEK CHANGED CELL 37 F= $2.00 <--GOAL SEEK SET CELL 38 =FV(5%,n,,-1) 39 40 41 c i= 10.00% 42 43 APPR 1 APPR 2 APPR 3 44 7.20000 F|P 10%,7 1.94872 7.27254 45 =72/(100*0.10) F|P 10%,8 2.14359 =LOG(2)/LOG(1+0.10) 46 INTERPOLATING 7.26315 47 =7+(2-1.94872)/(2.14359-1.94872) 48 49 APPR 4 APPR 5 50 7.27254 n= 7.27254 <--SOLVER CHANGED CELL 51 =NPER(10%,,-1,2) F= $2.00 <--SOLVER TARGET CELL 52 =FV(10%,n,,-1) 53 54 APPR 6 55 n= 7.27432 <--GOAL SEEK CHANGED CELL 56 F= $2.00 <--GOAL SEEK SET CELL 57 =FV(5%,n,,-1)

58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95

i= APPR 1 4.80000 =72/(100*0.15)

APPR 4 4.95948 =NPER(15%,,-1,2)

APPR 6 n= F=

i= APPR 1 3.60000 =72/(100*0.20)

APPR 4 3.80178 =NPER(20%,,-1,2)

APPR 6 n= F=

15.00% APPR 2 F|P 15%,4 1.74901 F|P 15%,5 2.01136 INTERPOLATING 4.95670 =4+(2-1.74901)/(2.01136-1.74901) APPR 5 n= F=

4.95948 $2.00 =FV(15%,n,,-1)

APPR 3 4.95948 =LOG(2)/LOG(1+0.15)

<--SOLVER CHANGED CELL <--SOLVER TARGET CELL

4.96242 <--GOAL SEEK CHANGED CELL $2.00 <--GOAL SEEK SET CELL =FV(5%,n,,-1)

20.00% APPR 2 F|P 20%,3 1.72800 F|P 20%,4 2.07360 INTERPOLATING 3.78704 =3+(2-1.728)/(2.0736-1.728) APPR 5 n= F=

3.80178 $2.00 =FV(20%,n,,-1)

APPR 3 3.80178 =LOG(2)/LOG(1+0.20)

<--SOLVER CHANGED CELL <--SOLVER TARGET CELL

3.80304 <--GOAL SEEK CHANGED CELL $2.00 <--GOAL SEEK SET CELL =FV(5%,n,,-1)

A B C D E F G 1 PROBLEM 2.50 2 3 P= $176,000.00 4 n= 9 5 F= $525,000.00 6 7 USING COMPOUND INTEREST FORMULAS THIS IS 8 F=P*(1+i)^n 9 SOLVING FOR i 10 i=(F/P)^(1/n)-1 11 12 i= 12.9116% =(525000/176000)^(1/9)-1 13 14 15 OR, CAN USE RATE FUNCTION 16 P= $176,000.00 17 n= 9 18 F= $525,000.00 19 20 i= 12.9116% =RATE(9,,-176000,525000) 21 22 23 OR, CAN USE SOLVER 24 P= $176,000.00 25 n= 9 26 27 i= 12.9116% <--SOLVER CHANGED CELL 28 29 30 F= $525,000.00 <--SOLVER TARGET CELL 31 USING COMPOUND INTEREST FORMULAS THIS IS 32 =$176000.00*(1+i)^9 33 34 F= $525,000.00 COULD HAVE USED THIS AS SOLVER TARGET CELL 35 USING EXCEL'S FV FUNCTION THIS IS 36 =FV(i%,9,,-176000)

A B C D E F G 1 PROBLEM 2.51 2 3 i= 8.50% 4 n= 10-4= 6 5 P= $5,000.00 6 7 FINDING FW AT END OF YEAR 10 OF DEPOSIT AT END OF YEAR 4 8 9 F= $8,157.34 USING ELECTRONIC INTEREST TABLES THIS IS 10 =$5,000*(F|P 8.5%,6) 11 12 F= $8,157.34 USING COMPOUND INTEREST FORMULAS THIS IS 13 =5000*(1+0.085)^6 14 15 F= $8,157.34 USING EXCEL'S FV FUNCTION THIS IS 16 =FV(8.5%,6,,-5000)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

A PROBLEM 2.52

i= n= F=

12.00% 40 $15,000,000.00

TO FIND THE SINGLE SUM OF MONEY DEPOSITED TODAY, FIND THE PW OF THE DESIRED FUTURE AMOUNT P=

$161,201.97 USING COMPOUND INTEREST FORMULAS THIS IS =6000/(1+0.12)^40

$161,250.00 USING INTEREST TABLES THIS IS =$15,000,000*(P|F 12%,40)

$161,201.97 USING EXCEL'S PV FUNCTION THIS IS =PV(12%,40,,-15000000)

A B C D 1 PROBLEM 2.53 2 3 i= 7.50% COMPOUNDED ANNUALLY 4 n= 10 5 6 EOY DEPOSIT 7 0 $5,000.00 8 1 $1,000.00 9 2 $1,000.00 10 11 FIND THE FW OF EACH DEPOSIT AT YEAR 10 12 F= $14,005.87 USING COMPOUND INTEREST FORMULAS THIS IS 13 =5000*(1+0.075)^10+1000*(1+0.075)^9+1000*(1+0.075)^8 14 15 FIND THE FW OF EACH DEPOSIT AT YEAR 10 16 F= $14,005.87 USING ELECTRONIC INTEREST TABLES THIS IS 17 =$5,000*(F|P 7.5%,10)+$1,000*(F|P 7.5%,9)+$1,000*(F|P 7.5%,8) 18 19 FIND THE FW OF EACH DEPOSIT AT YEAR 10 20 F= $14,005.87 USING EXCEL'S FV FUNCTION THIS IS 21 =FV(7.5%,10,,-5000)+FV(7.5%,9,,-1000)+FV(7.5%,8,,-1000) 22 23 SUM THE PW OF EACH DEPOSIT AND THEN FIND ITS FW 24 F= $14,005.87 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS 25 =FV(7.5%,10,,-(NPV(7.5%,1000,1000)+5000))

A B C D E F G 1 PROBLEM 2.54 2 3 i= 6.00% COMPOUNDED ANNUALLY 4 n= 15 5 6 EOY DEPOSIT 7 0 $2,000.00 8 1 $0.00 9 2 $3,000.00 10 3 $0.00 11 4 $0.00 12 5 $4,000.00 13 6 $0.00 14 7 $1,000.00 15 16 17 FIND THE FW OF EACH DEPOSIT AT YEAR 15 18 F= $19,949.14 USING COMPOUND INTEREST FORMULAS THIS IS 19 =2000*(1+0.06)^15+3000*(1+0.06)^13+4000*(1+0.06)^10+1000*(1+0.06)^8 20 21 FIND THE FW OF EACH DEPOSIT AT YEAR 15 22 F= $19,949.16 USING INTEREST TABLES THIS IS 23 =$2,000*(F|P 6%,15)+$3,000*(F|P 6%,13)+$4,000*(F|P 6%,10)+$1,000*(F|P 6 24 25 FIND THE FW OF EACH DEPOSIT AT YEAR 15 26 F= $19,949.14 USING EXCEL'S FV FUNCTION THIS IS 27 =FV(6%,15,,-2000)+FV(6%,13,,-3000)+FV(6%,10,,-4000)+FV(6%,8,,-1000) 28 29 SUM THE PW OF EACH DEPOSIT AND THEN FIND ITS FW 30 F= $19,949.14 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS 31 =FV(6%,15,,-(NPV(6%,0,3000,0,0,4000,0,1000)+2000))

H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

A B C D E F G H I J K 1 PROBLEM 2.55 2 3 i= 7.00% COMPOUNDED ANNUALLY 4 n= 11 5 6 EOY 0 1 2 3 4 5 6 7 8 7 DEP/WDL $2,000.00 $0.00 $0.00 -$1,000.00 $0.00 $3,000.00 $0.00 $0.00 $1,500.00 8 9 FIND THE FW OF EACH DEPOSIT OR WITHDRAWAL AT YEAR 11 10 F= $8,831.27 USING COMPOUND INTEREST FORMULAS THIS IS =2000*(1+0.07)^111000*(1+0.07)^8+3000*(1+0.07)^6+1500*(1+0.07)^3 11 12 13 FIND THE FW OF EACH DEPOSIT OR WITHDRAWAL AT YEAR 11 14 F= $8,831.26 USING INTEREST TABLES THIS IS =$2,000*(F|P 7%,11)-$1,000*(F|P 7%,8)+$3,000*(F|P 7%,6)+$1,500*(F|P 7%,3) 15 16 17 FIND THE FW OF EACH DEPOSIT OR WITHDRAWAL AT YEAR 11 18 F= $8,831.27 USING EXCEL'S FV FUNCTION THIS IS =FV(7%,11,,-2000)+FV(7%,8,,1000)+FV(7%,6,,3000)+FV(7%,3,,-1500) 19 20 21 SUM THE PW OF EACH DEPOSIT OR WITHDRAWAL AND THEN FIND ITS FW 22 F= $4,209.70 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS 23 =FV(7%,11,,-(NPV(7%,0,0,-1000,0,3000,0,0,1500)+2000))

A 1 PROBLEM 2.56 2 3 4 5 6 7 8 9 10 a

i= n=

6.50% 7

EOY NCF

0 $0.00

$150.76 USING EXCEL'S FV FUNCTION THIS IS =FV(6.5%,6,,500)+FV(6.5%,5,,-200)+FV(6.5%,4,,400)+FV(6.5%,3,,300)+FV(6.5%,2,,-500)+FV(6.5%,1,,200)+100 $150.76 USING ELECTRONIC INTEREST TABLES THIS IS =-$500*(F|P 6.5%,6)+$200*(F|P 6.5%,5)+$400*(F|P 6.5%,4)300*(F|P 6.5%,3)+500*(F|P 6.5%,2)-200*(F|P 6.5%,1)+100

11 12

1 2 3 4 5 6 7 -$500.00 $200.00 $400.00 -$300.00 $500.00 -$200.00 $100.00

13 14 15 16 17

18 19 20 21 22 23 24

$97.02 USING EXCEL'S NPV FUNCTION THIS IS =NPV(6.5%,-500,200,400,-300,500,-200,100)+0 $97.02 USING ELECTRONIC INTEREST TABLES THIS IS =-$500*(P|F 6.5%,1)+$200*(P|F 6.5%,2)+$400*(P|F 6.5%,3)$300*(P|F 6.5%,4)+$500*(P|F 6.5%,5)-$200*(P|F 6.5%,6)+$100*(P|F 6.5%,7)

$97.02

CONVERTING THE FW TO PW USING EXCEL'S PV FUNCTION =PV(6.5%,7,,-150.76) $97.02 USING ELECTRONIC INTEREST TABLES THIS IS =$150.76*(P|F 6.5%,7)

A B C D E F G H I J 1 PROBLEM 2.57 2 3 i= 8.00% 4 n= 6 5 6 EOY 0 1 2 3 4 5 6 7 NCF $0.00 $500.00 -$200.00 $600.00 $300.00 -$100.00 $200.00 8 9 a P= $1,046.28 USING EXCEL'S NPV FUNCTION THIS IS 10 =NPV(6.5%,-500,200,400,-300,500,-200,100)+0 11 $1,046.28 USING INTEREST TABLES THIS IS =$500*(P|F 8%,1)-$200*(P|F 8%,2)+$600*(P|F 8%,3)+$300*(P|F 8%,4)-$100*(P|F 8%,5)+$200*(P|F 8%,6) 12 13 14 b F= $1,660.31 USING EXCEL'S FV FUNCTION THIS IS =FV(6.5%,6,,500)+FV(6.5%,5,,-200)+FV(6.5%,4,,15 400)+FV(6.5%,3,,300)+FV(6.5%,2,,-500)+FV(6.5%,1,,200)+100 16 $1,660.31 USING INTEREST TABLES THIS IS =$500*(F|P 8%,5)-$200*(F|P 8%,4)+$600*(F|P 8%,3)+$300*(F|P 8%,2)-$100*(F|P 8%,1)+$200 17 18 19 c P= $1,046.28 CONVERTING THE FW TO PW USING EXCEL'S PV FUNCTION 20 =PV(8%,6,,-1660.31) 21 $1,046.28 USING INTEREST TABLES THIS IS 22 =$1,660.31*(P|F 8%,6) 23 24 d FIND THE WORTH AT EOY 4 25 F4= $1,423.45 USING EXCEL'S PV AND FV FUNCTIONS THIS IS =FV(8%,3,,-500)+FV(8%,2,,200)+FV(8%,1,,26 600)+300+PV(8%,1,,100)+PV(8%,2,,-200) 27 $1,423.45 USING INTEREST TABLES THIS IS =$500*(F|P 8%,3)-200*(F|P 8%,2)+600*(F|P 8%,1)+$300-$100*(P|F 28 8%,1)+$200*(P|F 8%,2) 29 30 e CONVERT THE WORTH AT EOY 4 TO PRESENT 31 P= $1,046.28 USING EXCEL'S PV FUNCTION THIS IS 32 =PV(8%,4,,-1423.45) 33 $1,046.28 USING INTEREST TABLES THIS IS 34 =$1,423.45*(P|F 8%,4)

A B C D E F G H I J K 1 PROBLEM 2.58 2 3 i= 6.00% 4 5 a $8,000 6 7 8 9 10 11 12 13 14 0 1 2 3 4 5 6 7 8 15 16 17 $X $X+100 $X+400 18 19 $2X b TO SOLVE FOR THE VALUE OF X, SET UP THE PRESENT WORTH OF RENALDO'S PAYMENTS AS A FUNCTION OF X AND LET X BE ANY MONETARY VALUE FOR NOW. 20 THEN, USE SOLVER TO SET THE PW OF PAYMENTS EQUAL TO $8,000. 21 22 X= $2,272.61 <--SOLVER CHANGED CELL 23 24 P= $8,000.00 <--SOLVER TARGET CELL 25 USING EXCEL'S PV AND NPV FUNCTIONS THIS IS 26 =PV(6%,4,,-NPV(6%,X,X+100,X+400,2*X)) 27 28 CAN ALSO SOLVE USING INTEREST TABLES. 29 30 P= $8,000 USING INTEREST TABLES THIS IS 31 =$X*(P|F 6%,5)+($X+$100)*(P|F 6%,6)+($X+$400)*(P|F 6%,7)+$2X*(P|F 6%,8) 32 =$X*(0.74726)+($X+$100)*(0.70496)+($X+$400)*(0.66506)+$2X*(0.62741) 33 =3.37210*X+$336.52 34 X= $2,272.61 =(8000-336.52)/3.3721 35 36 c EOY PAYMENT 37 5 $2,272.61 $X 38 6 $2,372.61 $X+100 39 7 $2,672.61 $X+400 40 8 $4,545.23 $2X

L 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

A B C D E F G H I J 1 PROBLEM 2.59 2 i= 5.50% 3 4 5 6 $5X 7 8 a $4X 9 10 $3X 11 12 $2X 13 14 $X 15 16 17 0 1 2 3 4 5 6 7 8 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 -$20,000.00 38 39 b TO SOLVE FOR THE VALUE OF X, SET UP THE PRESENT WORTH OF REX'S PAYMENTS AS A FUNCTION OF X AND LET X BE ANY MONETARY VALUE FOR NOW. THEN, USE SOLVER TO SET THE PW OF PAYMENTS EQUAL TO $20,000. 40 41 42 X= $1,900.97 <--SOLVER CHANGED CELL 43 44 P= $20,000.00 <--SOLVER TARGET CELL 45 USING EXCEL'S PV AND NPV FUNCTIONS THIS IS 46 =PV(5.5%,3,,-NPV(5.5%,X,2*X,3*X,4*X,5*X)) 47 48 CAN ALSO SOLVE USING INTEREST TABLES. 49 50 P= $20,000 USING ELECTRONIC INTEREST TABLES THIS IS =$X*(P|F 5.5%,4)+$2*X*(P|F 5.5%,5)+$3*X*(P|F 51 5.5%,6)+$4*X*(P|F 5.5%,7)+$5*X*(P|F 5.5%,8) =$X*(0.807216743)+$2*X*(0.765134354)+$3*X*(0.725245833)+$4 52 *X*(0.687436809)+$5*X*(0.651598871) 53 =10.52099*X

54 55 56 57 58 59 60 61 62 63 64 65

B X=

C D $1,900.97

EOY 4 5 6 7 8

PAYMENT $1,900.97 $3,801.93 $5,702.90 $7,603.87 $9,504.83

SUM INTEREST

$28,514.50 $8,514.50

E F G =20000/10.520964541

=28,514.50-20,000.00 AMOUNT OF KEN'S CHECK

K 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 REX'S PAYMENTS AS THEN, USE SOLVER 40 41 42 43 44 45 46 47 48 49 50 P|F 8) 51 *X*(0.725245833)+$4 52 53

A B C D E F G H I J K 1 PROBLEM 2.60 2 3 i= 8.00% 4 n= 8 5 6 EOY 0 1 2 3 4 5 6 7 8 7 NCF $300.00 $300.00 $600.00 -$500.00 -$300.00 $0.00 $800.00 $700.00 $600.00 8 9 a P= $1,711.50 USING EXCEL'S NPV FUNCTION THIS IS 10 =NPV(8%,300,600,-500,-300,0,800,700,600)+300 11 $1,711.50 USING INTEREST TABLES THIS IS =$300+$300*(P|F 8%,1)+$600*(P|F 8%,2)-$500*(P|F 8%,3)-$300*(P|F 12 8%,4)+$800*(P|F 8%,6)+$700*(P|F 8%,7)+$600*(P|F 8%,8) 13 14 b F= $3,167.86 USING EXCEL'S FV FUNCTION THIS IS 15 =FV(8%,C4,,-C9) 16 F= $3,167.86 USING INTEREST TABLES THIS IS 17 =$1,711.50*(F|P 8%,8) 18 19 c F2= $1,996.29 USING EXCEL'S FV FUNCTION THIS IS 20 =FV(8%,2,,-1711.5) 21 F2= $1,996.29 USING INTEREST TABLES THIS IS 22 =$1,711.50*(F|P 8%,2)

1 2 3 4 5 6 7 8 9

A PROBLEM 2.61

17 18 19 20 21 22 23 24 25 26 27 28

i= n=

5.00% 8

EOY NCF

0 $150.00

10 11 12 13 14 15 16

1 $300.00

2 3 4 5 6 7 8 $450.00 $0.00 -$500.00 $0.00 $600.00 $700.00 $800.00

$1,919.20 USING COMPOUND INTEREST FORMULAS THIS IS =150+300*(1+0.05)^-1+450*(1+0.05)^-2-500*(1+0.05)^4+600*(1+0.05)^-6+700*(1+0.05)^-7+800*(1+0.05)^-8 $1,919.21 P= USING INTEREST TABLES THIS IS =$150+$300*(P|F 5%,1)+$450*(P|F 5%,2)-$500*(P|F 5%,4)$600*(P|F 5%,6)+$700*(P|F 5%,7)+$800*(P|F 5%,8) P= $1,919.20 USING EXCEL'S NPV FUNCTION THIS IS =NPV(5%,300,450,0,-500,0,600,700,800)+150

$2,835.54 USING COMPOUND INTEREST FORMULAS THIS IS =150*(1+0.05)^8+300*(1+0.05)^7+450*(1+0.05)^6500*(1+0.05)^4+600*(1+0.05)^2+700*(1+0.05)^1+800 $2,835.55 USING INTEREST TABLES THIS IS =$1,919.20*(F|P 5%,8) $2,835.54 USING EXCEL'S FV FUNCTION THIS IS =FV(5%,8,,-1919.20)

F6= $2,571.92 USING COMPOUND INTEREST FORMULAS THIS IS =150*(1+0.05)^6+300*(1+0.05)^5+450*(1+0.05)^4500*(1+0.05)^2+600+700*(1+0.05)^-1+800*(1+0.05)^-2 F6= $2,571.93 USING INTEREST TABLES THIS IS =$1,919.20*(F|P 5%,6) F6= $2,571.92 USING EXCEL'S FV FUNCTION THIS IS =FV(5%,6,,-1919.20)

A 1 PROBLEM 2.62 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

19 20 21

i= COST PAYMENT METHOD 1 GET CASH DISCOUNT= PW=

12.00% $30,000.00

3.00% $29,100.00 =30000*(1-0.03)

PAYMENT METHOD 2 PAY ACCORDING TO THE FOLLOWING SCHEDULE EOY 0 1 2 3 4 5 CF $5,000.00 $8,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00 PW= PW=

$28,414.37 USING EXCEL'S NPV FUNCTION THIS IS =NPV(12%,8000,6000,6000,6000,6000)+5000 $28,414.40 USING INTEREST TABLES THIS IS =$5,000+$8,000*(P|F 12%,1)+$6,000*(P|F 12%,2)+$6,000*(P|F 12%,3)+$6,000*(P|F 12%,4)+$6,000*(P|F 12%,5)

USE PAYMENT METHOD 2 - LOWER PW

A 1 PROBLEM 2.63 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

P|A

FACTOR

i= 8.00% USING 8% FOR EXAMPLE CALC n= 8 USING 8 FOR EXAMPLE CALC (P|A i%,n)= 5.74664 USING COMPOUND INTEREST FORMULAS THIS IS =((1+0.08)^8-1)/(0.08*(1+0.08)^8)

A|P

FACTOR

i= 3.00% USING 3% FOR EXAMPLE CALC n= 5 USING 5 FOR EXAMPLE CALC (A|P i%,n)= 0.21835 USING COMPOUND INTEREST FORMULAS THIS IS =(0.03*(1+0.03)^5)/((1+0.03)^5-1)

F|A

FACTOR

i= 10.00% USING 10% FOR EXAMPLE CALC n= 10 USING 10 FOR EXAMPLE CALC (F|A i%,n)= 15.93742 USING COMPOUND INTEREST FORMULAS THIS IS =((1+0.1)^10-1)/0.1

A|F

FACTOR

i= 3.00% USING 3% FOR EXAMPLE CALC n= 5 USING 5 FOR EXAMPLE CALC (A|F i%,n)= 0.18835 USING COMPOUND INTEREST FORMULAS THIS IS =0.03/((1+0.03)^5-1) ALL CHECK OK WITH APPENDIX A

A 1 PROBLEM 2.64 2 3 4 5 6 7 8 9 10 11 12

i= 9.00% n= 7 P= $40,000.00 A= $7,947.62 USING COMPOUND INTEREST FORMULAS THIS IS =40000*(0.09*(1+0.09)^7)/((1+0.09)^7-1) A= $7,947.60 USING INTEREST TABLES THIS IS 40,000*(A|P 9%,7) A= $7,947.62 USING EXCEL'S PMT FUNCTION THIS IS =PMT(0.09,7,-40000)

A 1 PROBLEM 2.65 2 3 4 5 6 7 8 9 10 11 12

i= n= A=

4.00% 10 $5,000.00

F= $60,030.54 USING COMPOUND INTEREST FORMULAS THIS IS =5000*((1+0.04)^10-1)/0.04 F= $60,030.55 USING INTEREST TABLES THIS IS =$5,000*(F|A 4%,10) F= $60,030.54 USING EXCEL'S FV FUNCTION THIS IS =FV(0.04,10,-5000)

A 1 PROBLEM 2.66 2 3 4 5 6 7 8 9 10 11 12

i= n= A=

6.00% 8 $7,500.00

P= $46,573.45 USING COMPOUND INTEREST FORMULAS THIS IS =7500*((1+0.06)^8-1)/(0.06*(1+0.06)^8) P= $46,573.43 USING INTEREST TABLES THIS IS =$7,500*(P|A 6%,8) P= $46,573.45 USING EXCEL'S PV FUNCTION THIS IS =PV(6%,8,-7500)

A 1 PROBLEM 2.67 2 3 4 5 6 7 8 9 10 11 12

i= 7.00% n= 35 F= $2,000,000.00 A= A= A=

$14,467.92 USING COMPOUND INTEREST FORMULAS THIS IS =2000000*0.07/((1+0.07)^35-1) $14,467.92 USING ELECTRONIC INTEREST TABLES THIS IS =$2,000,000*(A|F 7%,35) $14,467.92 USING EXCEL'S PMT FUNCTION THIS IS =PMT(0.07,35,,-2000000)

A 1 PROBLEM 2.68 2 3 4 5 6 7 8 9 10 11 12

i= 7.00% n= 5 P= $25,000.00 A= $6,097.27 USING COMPOUND INTEREST FORMULAS THIS IS =25000*(0.07*(1+0.07)^5)/((1+0.07)^5-1) A= $6,097.25 USING INTEREST TABLES THIS IS =$25,000*(A|P 7%,5) A= $6,097.27 USING EXCEL'S PMT FUNCTION THIS IS =PMT(0.07,5,-25000)

A 1 PROBLEM 2.69 2 3 a 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 b 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

i= n= A=

4.00% 20 $7,500.00

F= $223,335.59 USING COMPOUND INTEREST FORMULAS THIS IS =7500*((1+0.04)^20-1)/0.04 F= $223,335.60 USING INTEREST TABLES THIS IS =$7,500*(F|A 4%,20) F= $223,335.59 USING EXCEL'S FV FUNCTION THIS IS =FV(0.04,20,-7500)

i= n= A=

4.00% 25 $7,500.00

F= $312,344.31 USING COMPOUND INTEREST FORMULAS THIS IS =7500*((1+0.04)^25-1)/0.04 F= $312,344.33 USING INTEREST TABLES THIS IS =$7,500*(F|A 4%,25) F= $312,344.31 USING EXCEL'S FV FUNCTION THIS IS =FV(0.04,25,-7500)

i= n= A=

4.00% 30 $7,500.00

F= $420,637.03 USING COMPOUND INTEREST FORMULAS THIS IS =7500*((1+0.04)^30-1)/0.04 F= $420,637.05 USING INTEREST TABLES THIS IS =$7,500*(F|A 4%,30) F= $420,637.03 USING EXCEL'S FV FUNCTION THIS IS =FV(0.04,30,-7500)

i= n= A=

5.00% 20 $7,500.00

F= $247,994.66 USING COMPOUND INTEREST FORMULAS THIS IS =7500*((1+0.05)^20-1)/0.05 F= $247,994.63 USING INTEREST TABLES THIS IS =$7,500*(F|A 5%,20) F= $247,994.66 USING EXCEL'S FV FUNCTION THIS IS =FV(0.05,20,-7500)

i= n= A=

5.00% 25 $7,500.00

A 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97

B C D E F G H F= $357,953.24 USING COMPOUND INTEREST FORMULAS THIS IS =7500*((1+0.05)^25-1)/0.05 F= $357,953.25 USING INTEREST TABLES THIS IS =$7,500*(F|A 5%,25) F= $357,953.24 USING EXCEL'S FV FUNCTION THIS IS =FV(0.05,25,-7500)

i= n= A=

5.00% 30 $7,500.00

F= $498,291.36 USING COMPOUND INTEREST FORMULAS THIS IS =7500*((1+0.05)^30-1)/0.05 F= $498,291.38 USING INTEREST TABLES THIS IS =$7,500*(F|A 5%,30) F= $498,291.36 USING EXCEL'S FV FUNCTION THIS IS =FV(0.05,30,-7500) c

PERCENTAGE INCREASE FROM 20 TO 25 YEARS AT 4%= 39.85% =(312344.31-223335.59)/223335.59 PERCENTAGE INCREASE FROM 20 TO 30 YEARS AT 4%= 88.34% =(420637.03-223335.59)/223335.59 PERCENTAGE INCREASE FROM 20 TO 25 YEARS AT 5%= 44.34% =(357953.24-247994.66)/247994.66 PERCENTAGE INCREASE FROM 20 TO 30 YEARS AT 5%= 100.93% =(498291.36-247994.66)/247994.66 PERCENTAGE INCREASE FROM 4% TO 5% FOR 20 YEARS= 11.04% =(247994.66-223335.59)/223335.59 PERCENTAGE INCREASE FROM 4% TO 5% FOR 25 YEARS= 14.60% =(357953.24-312344.31)/312344.31 PERCENTAGE INCREASE FROM 4% TO 5% FOR 30 YEARS= 18.46% =(498291.36-420637.03)/420637.03

AT 4%, 25% AND 50% INCREASES IN YEARS YIELDED INCREASED ACCUMULATIONS OF 39.85% AT 5%, 25% AND 50% INCREASES IN YEARS YIELDED INCREASED ACCUMULATIONS OF 44.34% A 25% INCREASE IN INTEREST RATE YIELDED INCREASED ACCUMULATIONS OF 11.04%, 14.60%

I 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

I 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97

A B C D E F G H 1 PROBLEM 2.70 2 3 a i= 7.00% 4 n= 5 5 P= $50,000.00 6 7 WITH THE FIRST PAYMENT AT THE END OF YEAR 1 8 A= $12,194.53 USING COMPOUND INTEREST FORMULAS THIS IS 9 =50000*(0.07*(1+0.07)^5)/((1+0.07)^5-1) 10 A= $12,194.50 USING INTEREST TABLES THIS IS 11 =$50,000*(A|P 7%,5) 12 A= $12,194.53 USING EXCEL'S PMT FUNCTION THIS IS 13 =PMT(0.07,5,-50000) 14 15 16 b i= 7.00% 17 n= 5 PAYMENTS 18 t= 4 WITH FIRST PAYMENT AT EOY 4 19 P= $50,000.00 20 21 WITH THE FIRST PAYMENT AT THE END OF YEAR 4 22 FIND VALUE OF $50,000 AT EOY 3, THEN FIND AMOUNT OF 5 ANNUAL PAYMENTS 23 A= $14,938.83 USING COMPOUND INTEREST FORMULAS THIS IS 24 =50000*((1+0.07)^(4-1))*(0.07*(1+0.07)^5)/((1+0.07)^5-1) 25 A= $14,938.75 USING INTEREST TABLES THIS IS 26 =$50,000*(F|P 7%,3)*(A|P 7%,5) 27 A= $14,938.83 USING EXCEL'S PMT AND FV FUNCTIONS THIS IS 28 =PMT(7%,5,-FV(7%,4-1,,-50000))

A B C D E 1 PROBLEM 2.71 2 3 a i= 5.00% 4 n= 10 5 A= $5,000.00 6 7 WITH THE FIRST WITHDRAWAL AT THE END OF YEAR 1 8 P= $38,608.67 USING COMPOUND INTEREST FORMULAS THIS IS 9 =5000*((1+0.05)^10-1)/(0.05*(1+0.05)^10) 10 P= $38,608.65 USING INTEREST TABLES THIS IS 11 =$5,000*(P|A 5%,10) 12 P= $38,608.67 USING EXCEL'S PV FUNCTION THIS IS 13 =PV(5%,10,-5000) 14 15 16 b i= 5.00% 17 n= 10 WITHDRAWALS 18 t= 3 WITH FIRST WITHDRAWAL AT EOY 3 19 A= $5,000.00 20 21 WITH THE FIRST PAYMENT AT THE END OF YEAR 3 22 FIND VALUE OF 10 ANNUAL WITHDRAWALS AT EOY 2, THEN FIND PRESENT WORTH 23 24 P= $35,019.21 USING COMPOUND INTEREST FORMULAS THIS IS 25 =5000*((1+0.05)^10-1)/(0.05*(1+0.05)^10)*(1/(1+0.05)^(3-1)) 26 P= $35,019.20 USING INTEREST TABLES THIS IS 27 $5,000*(P|F 5%,2)*(P|A 5%,10) 28 P= $35,019.21 USING EXCEL'S PV FUNCTION THIS IS 29 =PV(5%,3-1,,-PV(5%,10,-5000))

F 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

A B C D E F G 1 PROBLEM 2.72 2 3 LET'S CONSIDER INTEREST RATES FROM 0% TO 20% 4 A= $10,000.00 $5,000.00 5 n= 5 10 6 7 PV OF PV OF 8 INTEREST 10K FOR 5 YR 5K FOR 10 YR 9 0.00% $50,000.00 =PV(0%,5,-10000) $50,000.00 =PV(0%,10,-5000) 10 1.00% $48,534.31 $47,356.52 11 2.00% $47,134.60 $44,912.93 12 3.00% $45,797.07 =PV(3%,5,-10000) $42,651.01 =PV(3%,10,-5000) 13 4.00% $44,518.22 $40,554.48 14 5.00% $43,294.77 $38,608.67 15 6.00% $42,123.64 $36,800.44 16 7.00% $41,001.97 $35,117.91 17 8.00% $39,927.10 $33,550.41 18 9.00% $38,896.51 $32,088.29 19 10.00% $37,907.87 $30,722.84 20 11.00% $36,958.97 $29,446.16 21 12.00% $36,047.76 $28,251.12 22 13.00% $35,172.31 $27,131.22 23 14.00% $34,330.81 $26,080.58 24 15.00% $33,521.55 $25,093.84 25 16.00% $32,742.94 $24,166.14 26 17.00% $31,993.46 $23,293.02 27 18.00% $31,271.71 $22,470.43 28 19.00% $30,576.35 $21,694.67 29 20.00% $29,906.12 =PV(20%,5,-10000) $20,962.36 =PV(20%,10,-5000) 30 31 PREFER TO RECEIVE YOUR MONEY QUICKER AT $10K FOR EACH OF 5 YEARS 32 33 PREFER TO PAY YOUR MONEY OVER A LONGER PERIOD AT $5K FOR EACH OF 10 YEARS

H 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 OR EACH OF33 10 YEARS

1 2 3 4 5 6 7

A PROBLEM 2.73

i= n= A(3 TO 10)= DISPLACED n=

6.00% 8 $10,000.00 2

30 31 32 33 34 35 36 37 38

39 40 41 42 43 44

NOTE THAT THESE CASH FLOWS ARE OVER THE SAME AMOUNT OF TIME, JUST DISPLACED 2 YEARS. THEREFORE, SIMPLY DETERMINE THE WORTH OF $10,000 TWO YEARS EARLIER

8 9 10 11 12 13 14 15 16

17 18 19 20 21 22 23 24 25 26 27 28 29

A(1 TO 8)= A(1 TO 8)= A(1 TO 8)=

$8,899.96 USING COMPOUND INTEREST FORMULAS THIS IS =10000/(1+0.06)^2 $8,900.00 USING INTEREST TABLES THIS IS =$10,000*(P|F 6%,2) $8,899.96 USING EXCEL'S PV FUNCTION THIS IS =PV(6%,2,,-10000)

OR, CAN DETERMINE THE PW OF THE CASH FLOW SERIES FROM YEARS 3-10 AND THEN DETERMINE THE EQUIVALENT AMOUNT OF THE SERIES FROM YEARS 1-8. A(1 TO 8)= A(1 TO 8)=

i= n= A(3 TO 10)= DISPLACED n=

$8,900.22 USING INTEREST TABLES THIS IS =$10,000*(P|A 6%,8)*(P|F 6%,2)*(A|P 6%,8) $8,899.96 USING EXCEL'S PMT AND PV FUNCTIONS THIS IS =PMT(6%,8,-PV(6%,2,,-PV(6%,8,-10000)))

10.00% 8 $10,000.00 2

NOTE THAT THESE CASH FLOWS ARE OVER THE SAME AMOUNT OF TIME, JUST DISPLACED 2 YEARS. THEREFORE, SIMPLY DETERMINE THE WORTH OF $10,000 TWO YEARS EARLIER A(1 TO 8)= A(1 TO 8)= A(1 TO 8)=

$8,264.46 USING COMPOUND INTEREST FORMULAS THIS IS =10000/(1+0.10)^2 $8,264.50 USING INTEREST TABLES THIS IS =$10,000*(P|F 10%,2) $8,264.46 USING EXCEL'S PV FUNCTION THIS IS =PV(10%,2,,-10000)

OR, CAN DETERMINE THE PW OF THE CASH FLOW SERIES FROM YEARS 3-10 AND THEN DETERMINE THE EQUIVALENT AMOUNT OF THE SERIES FROM YEARS 1-8. A(1 TO 8)= A(1 TO 8)=

$8,264.46 USING EXCEL'S PMT AND PV FUNCTIONS THIS IS =PMT(10%,8,-PV(10%,2,,-PV(10%,8,-10000))) $8,264.33 USING INTEREST TABLES THIS IS =$10,000*(P|A 10%,8)*(P|F 10%,2)*(A|P 10%,8)

1 2 3 4 5 6 7

A PROBLEM 2.74

i= n= A(3 TO 10)= DISPLACED n=

6.00% 10 $10,000.00 10

30 31 32 33 34 35 36 37 38

39 40 41 42 43 44

NOTE THAT THESE CASH FLOWS ARE OVER THE SAME AMOUNT OF TIME, JUST DISPLACED 10 YEARS. THEREFORE, SIMPLY DETERMINE THE WORTH OF $10,000 10 YEARS LATER

8 9 10 11 12 13 14 15 16

17 18 19 20 21 22 23 24 25 26 27 28 29

A(11 TO 20)= A(11 TO 20)= A(11 TO 20)=

$17,908.48 USING COMPOUND INTEREST FORMULAS THIS IS =10000*(1+0.06)^2 $17,908.50 USING INTEREST TABLES THIS IS =$10,000*(F|P 6%,10) $17,908.48 USING EXCEL'S FV FUNCTION THIS IS =FV(6%,10,,-10000)

OR, CAN DETERMINE THE FW OF THE CASH FLOW SERIES FROM YEARS 1-10 AND THEN DETERMINE THE EQUIVALENT AMOUNT OF THE SERIES FROM YEARS 11-20. A(11 TO 20)= A(11 TO 20)=

i= n= A(3 TO 10)= DISPLACED n=

$17,908.74 USING INTEREST TABLES THIS IS =$10,000*(F|A 6%,10)*(A|P 6%,10) $17,908.48 USING EXCEL'S PMT AND PV FUNCTIONS THIS IS =PMT(6%,10,-FV(6%,10,,-PV(6%,10,-10000)))

10.00% 10 $10,000.00 10

NOTE THAT THESE CASH FLOWS ARE OVER THE SAME AMOUNT OF TIME, JUST DISPLACED 10 YEARS. THEREFORE, SIMPLY DETERMINE THE WORTH OF $10,000 10 YEARS LATER A(11 TO 20)= A(11 TO 20)= A(11 TO 20)=

$25,937.42 USING COMPOUND INTEREST FORMULAS THIS IS =10000*(1+0.10)^2 $25,937.40 USING INTEREST TABLES THIS IS =$10,000*(F|P 10%,10) $25,937.42 USING EXCEL'S FV FUNCTION THIS IS =FV(10%,10,,-10000)

OR, CAN DETERMINE THE FW OF THE CASH FLOW SERIES FROM YEARS 1-10 AT EOY 10, AND THEN USE THAT AMOUNT AS A PW TO DETERMINE THE EQUIVALENT AMOUNT OF THE SERIES OVER YEARS 11-20. A(11 TO 20)= A(11 TO 20)=

$25,938.15 USING INTEREST TABLES THIS IS =$10,000*(F|A 10%,10)*(A|P 10%,10) $25,937.42 USING EXCEL'S PMT AND PV FUNCTIONS THIS IS =PMT(10%,10,-FV(10%,10,,-PV(10%,10,-10000)))

A 1 PROBLEM 2.75 2 3 4 5 6 7 8 9 10 11 12

i= n= A=

5.00% 10 $1,000.00

F= $12,577.89 USING COMPOUND INTEREST FORMULAS THIS IS =7500*((1+0.04)^20-1)/0.04 F= $12,577.89 USING INTEREST TABLES THIS IS =$1,000*(F|A 5%,10) F= $12,577.89 USING EXCEL'S FV FUNCTION THIS IS =FV(0.04,20,-7500)

A B C D E F G H 1 PROBLEM 2.76 2 3 a i= 8.00% 4 n= 8 5 A= $1,000.00 6 7 FINDING THE PW AT EOY 0 8 P= $5,746.64 USING COMPOUND INTEREST FORMULAS THIS IS 9 =1000*((1+0.08)^8-1)/(0.08*(1+0.08)^8) 10 P= $5,746.64 USING INTEREST TABLES THIS IS 11 =$1,000*(P|A 8%,8) 12 P= $5,746.64 USING EXCEL'S PV FUNCTION THIS IS 13 =PV(8%,8,-1000) 14 15 b i= 8.00% 16 n= 8 17 A= $1,000.00 18 19 FINDING THE FW AT EOY 8 20 F= $10,636.63 USING COMPOUND INTEREST FORMULAS THIS IS 21 =1000*((1+0.08)^8-1)/0.08 22 F= $10,636.63 USING INTEREST TABLES THIS IS 23 =$1,000*(F|A 8%,8) 24 F= $10,636.63 USING EXCEL'S FV FUNCTION THIS IS 25 =FV(0.08,8,-1000) 26 27 28 c i= 8.00% 29 n= 8 30 A= $1,000.00 31 t= 11 THREE YEARS AFTER LAST DEPOSIT 32 33 FINDING THE FW AT EOY 11 34 F= $13,399.09 USING COMPOUND INTEREST FORMULAS THIS IS 35 =1000*(((1+0.08)^8-1)/0.08)*(1+0.08)^3 36 F= $13,399.07 USING INTEREST TABLES THIS IS 37 =$1,000*(F|A 8%,8)*F|P(8%,3) 38 F= $13,399.09 USING EXCEL'S FV FUNCTION THIS IS 39 =FV(8%,11,,PV(8%,8,1000))

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

A PROBLEM 2.77

A= i= n(investment)= n(withdrawal)=

$60,000.00 10.00% 19 1 YEAR BEFORE FIRST WITHDRAWAL 10 NUMBER OF WITHDRAWALS

FIRST, FIND THE PW AT EOY 19 OF THE ANNUAL WITHDRAWALS. THEN, FIND THE PW AT EOY 0. P= $60,281.15 USING COMPOUND INTEREST FORMULAS THIS IS =60000*((1+0.1)^10-1)/(0.1*(1+0.1)^10)*(1+0.1)^-19 P= $60,281.92 USING INTEREST TABLES THIS IS $60,000*(P|A 10%,10)*(P|F 10%,19) P= $60,281.15 USING EXCEL'S PV FUNCTION THIS IS =PV(10%,20,,-PV(10%,10,-60000)) b

A= i= n(investment)= n(withdrawal)=

$60,000.00 15.00% 19 1 YEAR BEFORE FIRST WITHDRAWAL 10 NUMBER OF WITHDRAWALS

FIRST, FIND THE PW AT EOY 19 OF THE ANNUAL WITHDRAWALS. THEN, FIND THE PW AT EOY 0. P= $21,158.72 USING COMPOUND INTEREST FORMULAS THIS IS =60000*((1+0.15)^10-1)/(0.15*(1+0.15)^10)*(1+0.15)^-19 P= $21,160.14 USING INTEREST TABLES THIS IS $60,000*(P|A 15%,10)*(P|F 15%,19) P= $21,158.72 USING EXCEL'S PV FUNCTION THIS IS =PV(15%,20,,-PV(15%,10,-60000))

A B C D E F G H 1 PROBLEM 2.78 2 3 i= 7.00% 4 n= 12 5 P= $200,000.00 6 7 WITH THE FIRST PAYMENT AT THE END OF YEAR 1 8 A= $25,180.40 USING COMPOUND INTEREST FORMULAS THIS IS 9 =200000*(0.07*(1+0.07)^12)/((1+0.07)^12-1) 10 A= $25,180.00 USING INTEREST TABLES THIS IS 11 =$200,000*(A|P 7%,12) 12 A= $25,180.40 USING EXCEL'S PMT FUNCTION THIS IS 13 =PMT(0.07,12,-200000)

A PROBLEM 2.79

A= i1= n1=

$4,000.00 5.00% 3

i2=

8.00%

7 8

n2=

1 2 3 4 5

9 10 11 12 13 14 15 16 17 18 19

$12,000.00 10.00% 10

i2=

5.00%

21 22

n2=

FIRST, FIND THE FW OF THE ANNUAL DEPOSITS AS OF THE TIME OF THE LAST SUCH DEPOSIT. THEN, FIND THE FW OF THAT SUM AT THE NEW RATE FOR THE ADDITIONAL INVESTMENT PERIOD. F= $221,394.73 USING COMPOUND INTEREST FORMULAS THIS IS =12000*(((1+10%)^10-1)/10%)*(1+5%)^3 F= $221,395.63 USING INTEREST TABLES THIS IS =$12,000*(F|A 10%,10)*(F|P 5%,5) F= $221,394.73 USING EXCEL'S FV FUNCTION THIS IS =FV(5%,3,,-FV(10%,10,-12000)) A= i1= n1=

$18,000.00 9.00% 5

i2=

7.00%

35 36

n2=

37 38 39 40 41 42 43

FIRST, FIND THE FW OF THE ANNUAL DEPOSITS AS OF THE TIME OF THE LAST SUCH DEPOSIT. THEN, FIND THE FW OF THAT SUM AT THE NEW RATE FOR THE ADDITIONAL INVESTMENT PERIOD. F= $18,528.23 USING COMPOUND INTEREST FORMULAS THIS IS =4000*(((1+5%)^3-1)/5%)*(1+8%)^5 F= $18,528.25 USING INTEREST TABLES THIS IS =$4,000*(F|A 5%,3)*(F|P 8%,5) F= $18,528.23 USING EXCEL'S FV FUNCTION THIS IS =FV(8%,5,,-FV(5%,3,-4000)) A= i1= n1=

23 24 25 26 27 28 29 30 31 32 33

FIRST, FIND THE FW OF THE ANNUAL DEPOSITS AS OF THE TIME OF THE LAST SUCH DEPOSIT. THEN, FIND THE FW OF THAT SUM AT THE NEW RATE FOR THE ADDITIONAL INVESTMENT PERIOD. F= $185,091.25 USING COMPOUND INTEREST FORMULAS THIS IS =18000*(((1+9%)^5-1)/9%)*(1+7%)^8 F= $185,091.64 USING INTEREST TABLES THIS IS =$18,000*(F|A 9%,5)*(F|P 7%,8) F= $185,091.25 USING EXCEL'S FV FUNCTION THIS IS =FV(7%,8,,-FV(9%,5,-18000))

A B 1 PROBLEM 2.80 2 3 a A= 4 i= 5 n= 6 7 F= 8 9 F= 10 11 F= 12 13 14 b A= 15 i= 16 n(deposits=) 17 n(more years) 18 19 F= 20 21 F= 22 23 F= 24 25 26 c 27 i= 28 A(1st)= 29 n(1st)= 30 A(2nd)= 31 n(2nd) 32 A(3rd)= 33 n(3rd)= 34 35 F= 36 37 38

$2,000.00 5.00% 15 $43,157.13 USING COMPOUND INTEREST FORMULAS THIS IS =2000*((1+0.05)^15-1)/0.05 $43,157.12 USING INTEREST TABLES THIS IS =$2,000*(F|A 5%,15) $43,157.13 USING EXCEL'S FV FUNCTION THIS IS =FV(5%,15,-2000) $3,000.00 8.00% 10 5 $63,856.54 USING COMPOUND INTEREST FORMULAS THIS IS =3000*(((1+0.08)^10-1)/0.08)*(1+0.08)^5 $63,856.61 USING INTEREST TABLES THIS IS =$3,000*(F|A 8%,10)*(F|P 8%,5) $63,856.54 USING EXCEL'S FV FUNCTION THIS IS =FV(8%,5,,-FV(8%,10,-3000))

8.00% $2,000.00 5 $4,000.00 5 $6,000.00 5 $95,010.53 TABLES =$2,000*(F|A 8%,5)*(F|P 8%,10)+$4,000*(F|A 8%,5)*(F|P 8%,5)+$6,000*(F|A 8%,5) $95,010.55 EXCEL =FV(8%,5,-6000)+FV(8%,5,,-FV(8%,5,4000))+FV(8%,5+5,,-FV(8%,5,-2000))

A B 1 PROBLEM 2.81 2 3 i= A 4 1= n1= 5

5.00% $1,200.00 YEARS 1-5 5 DEPOSITS YEARS 1-5

A2=

n2=

4 WITHDRAWALS YEARS 4-7

8 9 10 11 12 13

t2=

4 START TIME OF WITHDRAWALS

P= P=

-$700.00 YEARS 4-7

$3,051.18 USING INTEREST TABLES THIS IS =$1,200*(P|A 5%,5)-$700*(P|A 5%,4)*(P|F 5%,3) $3,051.18 USING EXCEL'S FV FUNCTION THIS IS =PV(5%,5,-1200)-PV(5%,3,,-PV(5%,4,-700))

A 1 PROBLEM 2.82 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

SINCE THE AMOUNT PAID IS NOT GIVEN, ANY AMOUNT WILL SERVE TO ANSWER THE PROBLEM. A VALUE OF $1.00 IS SELECTED HERE P= $1.00 i= 7.000% A= $0.20 20% OF P n=

6.367 USING EXCEL'S NPER FUNCTION THIS IS =NPER(7%,0.2,-1)

COULD ALSO USE SOLVER TO DETERMINE n

6.367 <--SOLVER CHANGED CELL

$1.00 <--SOLVER TARGET CELL USING EXCEL'S PV FUNCTION THIS IS =PV(7%,n,-0.2)

P= n= A=

$1.00 7 $0.20

i= 9.196% USING EXCEL'S RATE FUNCTION THIS IS =RATE(7,0.2,-1) COULD ALSO USE SOLVER TO DETERMINE i i= 9.196% <--SOLVER CHANGED CELL P=

$1.00 <--SOLVER TARGET CELL USING EXCEL'S PV FUNCTION THIS IS =PV(i%,7,-0.2)

A 1 PROBLEM 2.83 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

SINCE THE AMOUNT OF THE LOAN IS NOT GIVEN, ANY AMOUNT WILL SERVE TO ANSWER THE PROBLEM. A VALUE OF $6.00 IS SELECTED HERE. P= $6.00 n= 7 A= $1.00 i=

4.009% USING EXCEL'S RATE FUNCTION THIS IS =RATE(7,0.2,-1)

COULD ALSO USE SOLVER TO DETERMINE i i=

4.009% <--SOLVER CHANGED CELL

$6.00 <--SOLVER TARGET CELL USING EXCEL'S PV FUNCTION THIS IS =PV(i,7,-C6)

A B C D E F G H I 1 PROBLEM 2.84 2 3 i= 9.00% n = 4 25 NUMBER OF DEPOSITS 1 5 A= $4,000.00 6 t= 28 TIME OF FIRST WITHDRAWAL n = 7 30 NUMBER OF WITHDRAWALS 2 8 FIRST, DETERMINE THE AMOUNT IN THE ACCOUNT RIGHT AFTER THE LAST a DEPOSIT AT EOY 25. THEN, FIND THE FW OF THAT AMOUNT ONE YEAR 9 BEFORE THE FIRST WITHDRAWAL AT EOY 27 10 11 F27= $402,532.54 USING COMPOUND INTEREST FORMULAS THIS IS 12 =4000*(((1+0.09)^25-1)/0.09)*(1+0.09)^2 13 F27= $402,532.56 USING INTEREST TABLES THIS IS 14 =$4,000*(F|A 9%,25)*(F|P 9%,2) 15 F27= $402,532.54 USING EXCEL'S FV FUNCTION THIS IS 16 =FV(9%,28-25-1,,-FV(9%,25,-4000)) 17 b USING THE ANSWER TO PART a, FIND THE PAYMENT AMOUNT OVER THE WITHDRAWAL PERIOD 18 19 20 A= $39,181.05 USING COMPOUND INTEREST FORMULAS THIS IS 21 =402532.54*(0.09*(1+0.09)^30)/((1+0.09)^30-1) 22 A= $39,182.52 USING INTEREST TABLES THIS IS 23 =$402,532.54*(A|P 9%,30) 24 A= $39,181.05 USING EXCEL'S PMT FUNCTION THIS IS 25 =PMT(9%,30,-402532.54) 26 27 28 c FOR THE ACCOUNT TO LAST FOREVER, ONLY THE INTEREST MAY BE WITHDRAWN 29 30 A= $36,227.93 =402532.54*0.09

A 1 PROBLEM 2.85 2 3 4 5 6 7 8 a 9 10 11 12 13 14 15 b 16 17 c 18 19 d 20 21 22 23 24 25 26 27 28 29 30 31

i= n DEPOSITS= A= n WITHDRAWALS=

12.00% 30 $7,500.00 ($5,000 FROM YOU + $2,500 FROM EMPLOYER) 30

$1,809,995.13 USING COMPOUND INTEREST FORMULAS THIS IS =7500*(((1+0.12)^30-1)/0.12) $1,809,995.10 USING INTEREST TABLES THIS IS =$7,500*(F|A 12%,30) $1,809,995.13 USING EXCEL'S FV FUNCTION THIS IS =FV(12%,30,-7500)

F= F=

SUM(YOU)=

$150,000.00 =5000*30

SUM(EMPLOYER)=

$75,000.00 =2500*30

EARNINGS=

$1,584,995.13 $1,584,995.13

USING THE ANSWER TO PART a, FIND THE YEARLY AMOUNT OVER THE WITHDRAWAL PERIOD A= A= A=

$224,699.42 USING COMPOUND INTEREST FORMULAS THIS IS =1809995.13*(0.12*(1+0.12)^30)/((1+0.12)^30-1) $224,692.80 USING INTEREST TABLES THIS IS =$1,809,995.13*(A|P 12%,30) $224,699.42 USING EXCEL'S PMT FUNCTION THIS IS =PMT(12%,30,-1809995.13)

FOR THE ACCOUNT TO LAST FOREVER, ONLY THE INTEREST MAY BE WITHDRAWN INTEREST ONLY= $217,199.42 =1809995.13*0.12

A 1 PROBLEM 2.86 2 3 4 5 6 7 8 9 10 11 12 13 14 15

i= 6.00% P= $10,000.00 DEPOSIT AT EOY 0 A= -$1,000.00 WITHDRAWALS AT EOY 3-7 n1= 10 YEARS FROM DEPOSIT TO FINAL WITHDRAWAL n2= 5 YEARS OF WITHDRAWALS (3, 4, 5, 6, 7) n3=

YEARS FROM 5TH WITHDRAWAL TO FINAL WITHDRAWAL

FIND THE FW AT EOY 10 OF THE INITIAL DEPOSIT AND THE FIVE WITHDRAWALS F= $11,194.61 USING INTEREST TABLES THIS IS =$10,000*(F|P 6%,10)-$1,000*(F|A 6%,5)*(F|P 6%,3) F= $11,194.61 USING EXCEL'S FV FUNCTION THIS IS =FV(6%,10,,-10000)+FV(6%,3,,-FV(6%,5,-(-1000)))

A 1 PROBLEM 2.87 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

12.00%

P= A= n1= n2=

$15,000.00 LOAN VALUE AT EOY 0 $3,000.00 PAYMENTS AT EOY 1, 2, 3, 4 4 YEARS UNTIL FINAL A=$3,000 PAYMENT 1 ADDITIONAL YEARS UNTIL FINAL PAYMENT

FIND THE LOAN VALUE AT EOY 5 AND SUBTRACT OFF THE PAYMENT VALUES AT EOY 5. WHAT'S LEFT IS THE FINAL LOAN PAYMENT AT EOY 5. F= $10,376.58 USING COMPOUND INTEREST FORMULAS THIS IS =15000*(1+0.12)^(4+1)-(3000*(((1+0.12)^4-1)/0.12))*(1+0.12)^1 F= $10,376.55 USING INTEREST TABLES THIS IS =$15,000*(F|P 12%,5)-$3,000*(F|A 12%,4)*(F|P 12%,1) F= $10,376.58 USING EXCEL'S FV FUNCTION THIS IS =FV(12%,4+1,,-15000)+FV(12%,1,,-FV(12%,4,3000)) F=

$10,376.58 IS THE AMOUNT OF THE YEAR 5 PAYMENT

A B C D 1 PROBLEM 2.88 2 3 i= 9.00% 4 n1= 10 YEARS OF WITHDRAWALS n = 5 5 WITHDRAWALS REMAINING AT EOY 45 2 6 AMT45= $32,801.60 AMOUNT LEFT IN ACCT AT EOY 45 7 THE FOLLOWING WILL BE NEEDED IN THE LAST STEPS OF THE PROBLEM n3= 8 15 YEARS FROM DEPOSIT 1 TO EOY 40 n4= 9 10 YEARS FROM DEPOSIT 2 TO EOY 40 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

n5=

YEARS FROM DEPOSIT 3 TO EOY 40

FIRST, DETERMINE THE AMOUNT OF THE ANNUAL WITHDRAWALS A= $8,432.96 USING INTEREST TABLES THIS IS =$32,801.60*(A|P 9%,5) A= $8,433.04 USING EXCEL'S PMT FUNCTION THIS IS =PMT(9%,5,-32801.6) NOW KNOWING THE ANNUAL WITHDRAWAL, DETERMINE THE AMOUNT IN THE ACCOUNT AT EOY 40 AMT40= $54,120.41 USING INTEREST TABLES THIS IS =$8433.04*(P|A 9%,10) AMT40= $54,120.39 USING EXCEL'S PV FUNCTION THIS IS =PV(9%,10,-8433.04) NOW, DETERMINE THE VALUE AT EOY 40 OF THE THREE "$X" DEPOSITS AT EOY 25, 30, AND 35 AND SOLVE FOR X AMT40= =7.54846 USING INTEREST TABLES THIS IS TIMES X =(F|P 9%,15)+(F|P 9%,10)+(F|P 9%,5) TIMES X =(3.64248+2.36736+1.53862) TIMES X =7.54846 TIMES X X= $7,169.73 =$54,120.41/7.54846 AMT40=

7.54847 USING EXCEL'S FV FUNCTION THIS IS TIMES X =(FV(9%,15,,-1)+(FV(9%,10,,-1)+(FV(9%,5,,-1)))) X= $7,169.72 =54120.39/7.54847 ****************************************************** THIS PROBLEM MAY BETTER BE ANSWERED USING SOLVER LET X BE ANY VALUE AT THIS POINT. SET UP ALL FOLLOWING EQUATIONS AS IF THE VALUE OF X IS RIGHT. SOLVER WILL LATER BE USED TO CORRECTLY SEARCH FOR AND SET THE VALUE OF X X=

$7,169.73 <--SOLVER CHANGED CELL

SOLVE FOR THE AMOUNT OF THE THREE DEPOSITS AT EOY 40 AMT40= $54,120.44 USING INTEREST TABLES THIS IS X*(F|P 9%,15)+X*(F|P 9%,10)+X*(F|P 9%,5) NOW, SOLVE FOR THE ANNUAL WITHDRAWAL FROM EOY 41 TO 50 A= $8,433.05 =$54,120.84*(A|P 9%,10) =$54,120.84*0.15582 NOW, SOLVE FOR THE AMOUNT REMAINING IN THE ACCOUNT AT EOY 45 AMT45= $32,801.60 <--SOLVER TARGET CELL =$8,433.11*(P|A 9%,5)

$7,169.72 <--SOLVER CHANGED CELL

TIMES X

A 53 54 55 56 57 58 59 60 61 62 63

SOLVE FOR THE AMOUNT OF THE THREE DEPOSITS AT EOY 40 AMT40= $54,120.39 USING EXCEL'S FV FUNCTION THIS IS =(FV(9%,15,,-X)+FV(9%,10,,-X)+(FV(9%,5,,-X)) NOW, SOLVE FOR THE ANNUAL WITHDRAWAL FROM EOY 41 TO 50 A= $8,433.04 USING EXCEL'S PMT FUNCTION THIS IS =PMT(9%,10,-54120.91) NOW, SOLVE FOR THE AMOUNT REMAINING IN THE ACCOUNT AT EOY 45 AMT45= $32,801.60 <--SOLVER TARGET CELL USING EXCEL'S PV FUNCTION THIS IS =PV(9%,5,-8433.12)

P= i= i= i= n1=

$20,000.00 5% 6% 7% 10

AT EOY 30 YEARS 31-40 YEARS 41-50 YEARS 51 AND BEYOND YEARS AT 5%

n2=

YEARS AT 6%

n3=

YEARS AT 7%

n4=

YEARS OF WITHDRAWALS

11 12 13 14 15 16 17 18 19 20 21 22

n5=

YEARS OF WITHDRAWALS REMAINING AT EOY 65

1 2 3 4 5 6 7

23 24 25 26 27

A PROBLEM 2.89

FIRST, SOLVE FOR THE AMOUNT AVAILABLE AT EOY 60 AMT60= $114,767.37 USING INTEREST TABLES THIS IS =$20,000*(F|P 5%,10)*(F|P 6%,10)*(F|P 7%,10) A= $16,340.58 USING INTEREST TABLES THIS IS =$114,767.37*(A|P 7%,10) AMT60= $114,767.63 USING EXCEL'S FV FUNCTION THIS IS =FV(7%,10,,-FV(6%,10,,-FV(5%,10,,-20000))) A= $16,340.33 USING EXCEL'S PMT FUNCTION THIS IS =PMT(7%,10,-114767.63)

SOLVE FOR THE PW OF THE 5 REMAINING WITHDRAWALS AT EOY 66-70 PLUS THE WITHDRAWAL DUE AT EOY 65 WDL65= $83,340.22 USING INTEREST TABLES THIS IS =$16,340.58*(P|A 7%,5)+$16,340.58 WDL65= $83,338.90 USING EXCEL'S PV FUNCTION THIS IS =PV(7%,5,-16340.33)+16340.33

A B C D E F G H I J K 1 PROBLEM 2.90 2 3 i= 10.00% 4 n= 8 5 6 EOY 0 1 2 3 4 5 6 7 8 7 CF -$2,500.00 $3,000.00 $4,500.00 $0.00 -$5,000.00 $0.00 -$1,000.00 $7,000.00 $3,000.00 8 FIRST, FIND THE PW OF THIS CASH FLOW SERIES. THEN FIND THE EQUIVALENT 9 VALUE OF "A" 10 P= $4,958.43 USING INTEREST TABLES THIS IS =$2,500+$3,000*(P|F 10%,1)+$4,500*(P|F 10%,2)-$5,000*(P|F 10%,4)11 $1,000*(P|F 10%,6)+$7,000*(P|F 10%,7)+$3,000*(P|F 10%,8) 12 A= $929.41 USING INTEREST TABLES THIS IS 13 =$4,958.43*(A|P 10%,8) 14 P= $4,958.37 USING EXCEL'S NPV FUNCTION THIS IS 15 =NPV(10%,3000,4500,0,-5000,0,-1000,7000,3000)-2500 16 A= $929.42 USING EXCEL'S PMT FUNCTION THIS IS 17 =PMT(C3,C4,-C10)

A 1 PROBLEM 2.91 2 3 a 4 5 b 6 7 c 8 9 10 11 USING (a) 12 13 USING (b) 14

B*(F|P i%,1)*(F|A i%,n)

B*(1+i)*((1+i)^n-1)/i

B= n= i=

$1,000.00 5 10.00%

$6,715.61 USING INTEREST TABLES THIS IS =$1,000*(F|P 10%,1)*(F|P 10%,5) $6,715.61 USING COMPOUND INTEREST FORMULAS THIS IS =1000*(1+0.1)*((1+0.1)^5-1)/0.1

A B C D E F 1 PROBLEM 2.92 2 3 P|G FACTOR 4 5 i= 8.00% USING 8% FOR EXAMPLE CALC 6 n= 3 USING 3 FOR EXAMPLE CALC 7 P|G= 2.44500 USING COMPOUND INTEREST FORMULAS THIS IS 8 =(1-(1+3*0.08)*(1+0.08)^(-3))/(0.08^2) 9 10 11 F|G FACTOR NOT TABULATED IN APPENDIX A 12 13 i= 12.00% USING 12% FOR EXAMPLE CALC 14 n= 25 USING 25 FOR EXAMPLE CALC 15 F|G= 902.78225 USING COMPOUND INTEREST FORMULAS THIS IS 16 =((1+0.12)^25-(1+25*0.12))/(0.12^2) 17 18 19 A|G FACTOR 20 21 i= 10.00% USING 10% FOR EXAMPLE CALC 22 n= 10 USING 10 FOR EXAMPLE CALC 23 A|G= 3.72546 USING COMPOUND INTEREST FORMULAS THIS IS 24 =(1/0.10)-(10/0.10)*(0.10/((1+0.10)^10-1)) 25 26 P|G AND A|G CHECK OK WITH APPENDIX A

A B C D E F G H 1 PROBLEM 2.93 2 3 i= 5.00% 4 n= 5 A1= 5 $800.00 6 G= $100.00 7 8 P= $4,287.28 USING INTEREST TABLES THIS IS 9 =$800*(P|A 5%,5)+$100*(P|G 5%,5) 10 P= $4,287.27 USING EXCEL'S NPV FUNCTION 11 =NPV(5%,800,900,1000,1100,1200) 12 13 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 14 15 EOY CF 16 0 $0.00 17 1 $800.00 18 2 $900.00 19 3 $1,000.00 20 4 $1,100.00 21 5 $1,200.00 22 23 P= $4,287.27 =NPV(5%,800,900,1000,1100,1200)+0

A B C D E F G H 1 PROBLEM 2.94 2 3 i= 6.00% 4 n= 7 A1= $5,000.00 5 6 G= $1,000.00 7 8 FV= $65,199.79 USING INTEREST TABLES THIS IS 9 =($5,000*(P|A 6%,7)+$1,000*(P|G 6%,7))*F|P 6%,7 10 FV= $65,199.82 USING EXCEL'S FV AND NPV FUNCTIONS 11 =FV(6%,7,,-NPV(6%,5000,6000,7000,8000,9000,10000,11000)) 12 13 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 14 15 EOY CF 16 0 $0.00 17 1 $5,000.00 18 2 $6,000.00 19 3 $7,000.00 20 4 $8,000.00 21 5 $9,000.00 22 6 $10,000.00 23 7 $11,000.00 24 25 FV= $65,199.82 =FV(6%,7,,-(NPV(6%,5000,6000,7000,8000,9000,10000,11000)+0))

I 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

A B C D E F G H 1 PROBLEM 2.95 2 3 i= 8.00% 4 n= 6 A1= $12,000.00 5 6 G= -$2,000.00 7 8 P= $34,428.02 USING INTEREST TABLES THIS IS 9 =$12,000*(P|A 8%,6)-$2,000*(P|G 8%,6) 10 P= $34,428.01 USING EXCEL'S NPV FUNCTION 11 =NPV(8%,12000,10000,8000,6000,4000,2000) 12 13 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 14 15 EOY CF 16 0 $0.00 17 1 $12,000.00 18 2 $10,000.00 19 3 $8,000.00 20 4 $6,000.00 21 5 $4,000.00 22 6 $2,000.00 23 24 P= $34,428.01 =NPV(8%,12000,10000,8000,6000,4000,2000)+0

I 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

A B C D E F G H 1 PROBLEM 2.96 2 3 i= 10.00% 4 n= 4 A1= $2,000.00 5 6 G= $500.00 7 8 a P= $8,528.80 USING INTEREST TABLES THIS IS 9 =$2,000*(P|A 10%,4)+$500*(P|G 10%,4) 10 P= $8,528.79 USING EXCEL'S NPV FUNCTION 11 =NPV(10%,2000,2500,3000,3500) 12 13 b A= $2,690.58 USING INTEREST TABLES THIS IS 14 =$8,528.80*(A|P 10%,4) 15 A= $2,690.59 USING INTEREST TABLES THIS IS 16 =$2,000+$500*(A|G 10%,4) 17 A= $2,690.58 USING EXCEL'S PMT FUNCTION 18 =PMT(10%,4,-8528.79) 19 20 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 21 22 EOY CF 23 0 $0.00 24 1 $2,000.00 25 2 $2,500.00 26 3 $3,000.00 27 4 $3,500.00 28 29 P= $8,528.79 =NPV(10%,2000,2500,3000,3500)+0 30 31 A= $2,690.58 =PMT(10%,4,-8528.79)

I 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

A B C D E F G H I 1 PROBLEM 2.97 2 3 i= 12.00% 4 n= 6 A = 5 -$2,000.00 1 6 G= $1,000.00 7 8 P= $707.35 USING INTEREST TABLES THIS IS 9 -$2,000*(P|A 12%,6)+$1,000*(P|G 12%,6) 10 P= $707.36 USING EXCEL'S NPV FUNCTION THIS IS 11 =NPV(12%,-2000,-1000,0,1000,2000,3000) 12 13 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 14 15 EOY CF 16 0 $0.00 17 1 -$2,000.00 18 2 -$1,000.00 19 3 $0.00 20 4 $1,000.00 21 5 $2,000.00 22 6 $3,000.00 23 24 P= $707.36 =NPV(12%,-2000,-1000,0,1000,2000,3000)+0

A B C D E F G 1 PROBLEM 2.98 2 3 a i= 6.00% 4 n= 8 5 INITIAL CF= -$75,000.00 A1= 6 $3,000.00 7 G= $3,000.00 8 9 P= $3,154.11 USING INTEREST TABLES THIS IS 10 =-$75,000+3,000*(P|A 6%,8)+3,000*(P|G 6%,8) 11 P= $3,154.12 USING EXCEL'S NPV FUNCTION THIS IS

=NPV(6%,3000,3000+3000,3000+2*3000,3000+3*3000,3000 +4*3000,3000+5*3000,3000+6*3000,3000+7*3000)-75000

12 13 14 15 16 17 18 19 20 21 22 23 24 25

SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER EOY CF 0 -$75,000.00 1 $3,000.00 2 $6,000.00 3 $9,000.00 4 $12,000.00 5 $15,000.00 6 $18,000.00 7 $21,000.00 8 $24,000.00 P=

26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

$3,154.12 =NPV(6%,3000,6000,9000,12000,15000,18000,21000,24000 )-75000

i= 7.00% n= 8 INITIAL CF= -$75,000.00 A1= $3,000.00 G= $3,000.00 P= P=

-$719.28 USING INTEREST TABLES THIS IS =-$75,000+3,000*(P|A 7%,8)+3,000*(P|G 7%,8) -$719.29 USING EXCEL'S NPV FUNCTION THIS IS =NPV(7%,3000,3000+3000,3000+2*3000,3000+3*3000,3000 +4*3000,3000+5*3000,3000+6*3000,3000+7*3000)-75000

SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER EOY CF 0 -$75,000.00 1 $3,000.00 2 $6,000.00 3 $9,000.00 4 $12,000.00 5 $15,000.00 6 $18,000.00 7 $21,000.00 8 $24,000.00 P=

-$719.29 =NPV(7%,3000,6000,9000,12000,15000,18000,21000,24000 )-75000

A B C D E F G 1 PROBLEM 2.99 2 3 a i= 5.00% 4 n= 35 5 INITIAL CF= $0.00 A1= 6 $7,500.00 7 G= $1,000.00 8 9 FW= $1,783,808.45 USING ELECTRONIC INTEREST TABLES THIS IS 10 $0+$7,500*(F|A 5%,35)+$1,000*(P|G 5%,35)*(F|P 5%,35) 11 12 13 b i= 6.00% 14 n= 35 15 INITIAL CF= $0.00 A1= 16 $7,500.00 17 G= $1,000.00 18 19 FW= $2,109,673.85 USING ELECTRONIC INTEREST TABLES THIS IS 20 $0+$7,500*(F|A 6%,35)+$1,000*(P|G 6%,35)*(F|P 6%,35) 21 22 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 23 24 a FOR 5% b FOR 6% 25 EOY CF EOY CF 26 0 $0.00 0 $0.00 27 1 $7,500.00 1 $7,500.00 28 2 $8,500.00 2 $8,500.00 29 3 $9,500.00 3 $9,500.00 30 4 $10,500.00 4 $10,500.00 31 5 $11,500.00 5 $11,500.00 32 6 $12,500.00 6 $12,500.00 33 7 $13,500.00 7 $13,500.00 34 8 $14,500.00 8 $14,500.00 35 9 $15,500.00 9 $15,500.00 36 10 $16,500.00 10 $16,500.00 37 11 $17,500.00 11 $17,500.00 38 12 $18,500.00 12 $18,500.00 39 13 $19,500.00 13 $19,500.00 40 14 $20,500.00 14 $20,500.00 41 15 $21,500.00 15 $21,500.00 42 16 $22,500.00 16 $22,500.00

A 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63

B C D 17 $23,500.00 18 $24,500.00 19 $25,500.00 20 $26,500.00 21 $27,500.00 22 $28,500.00 23 $29,500.00 24 $30,500.00 25 $31,500.00 26 $32,500.00 27 $33,500.00 28 $34,500.00 29 $35,500.00 30 $36,500.00 31 $37,500.00 32 $38,500.00 33 $39,500.00 34 $40,500.00 35 $41,500.00 FW= $1,783,808.45 =FV(5%,35,,-NPV(5%,CF YR 1:CF YR 35)+0)

E F G 17 $23,500.00 18 $24,500.00 19 $25,500.00 20 $26,500.00 21 $27,500.00 22 $28,500.00 23 $29,500.00 24 $30,500.00 25 $31,500.00 26 $32,500.00 27 $33,500.00 28 $34,500.00 29 $35,500.00 30 $36,500.00 31 $37,500.00 32 $38,500.00 33 $39,500.00 34 $40,500.00 35 $41,500.00 FW= $2,109,673.85 =FV(6%,35,,-NPV(6%,CF YR 1:CF YR 35)+0)

A B C D E F G H 1 PROBLEM 2.100 2 3 i= 5.00% 4 n= 5 5 INITIAL CF= -$90,000.00 A1= 6 $30,000.00 7 G= -$3,000.00 8 9 PW= $15,173.64 USING INTEREST TABLES THIS IS 10 =-$90,000+$30,000*(P|A 5%,5)-$3,000*(P|G 5%,5) 11 PW= $15,173.55 USING EXCEL'S NPV FUNCTION THIS IS =NPV(5%,30000,30000-3000,30000-2*3000,300003*3000,30000-4*3000)-90000 12

A B C D E F G H 1 PROBLEM 2.101 2 3 a i= 6.00% 4 n= 7 5 INITIAL CF= $0.00 A1= 6 $7,000.00 7 G= -$1,000.00 8 9 EQ(t=5)= $31,618.32 USING INTEREST TABLES THIS IS 10 =($7,000*(P|A 6%,7)-$1,000*(P|G 6%,7))*(F|P 6%,5) 11 12 b i= 10.00% 13 n= 7 14 INITIAL CF= $0.00 A1= 15 $7,000.00 16 G= -$1,000.00 17 18 EQ(t=5)= $34,329.34 USING INTEREST TABLES THIS IS 19 =($7,000*(P|A 10%,7)-$1,000*(P|G 10%,7))*(F|P 10%,5) 20 21 22 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 23 24 a EOY CF b EOY CF 25 0 $0.00 0 $0.00 26 1 $7,000.00 1 $7,000.00 27 2 $6,000.00 2 $6,000.00 28 3 $5,000.00 3 $5,000.00 29 4 $4,000.00 4 $4,000.00 30 5 $3,000.00 5 $3,000.00 31 6 $2,000.00 6 $2,000.00 32 7 $1,000.00 7 $1,000.00 33 34 EQ(t=5)= $31,618.22 EQ(t=5)= $34,329.33 =FV(6%,5,,-NPV(6%,CF YR 1:CF YR =FV(10%,5,,-NPV(10%,CF YR 35 7)+0) 1:CF YR 7)+0)

A B C D E 1 PROBLEM 2.102 2 3 i= 12.00% 4 n= 8 5 INITIAL CF= -$50,000.00 A1= 6 $13,000.00 7 G= -$1,000.00 8 9 PW= $107.87 USING INTEREST TABLES THIS IS 10 =-$50,000+$13,000*(P|A 12%,8)-$1,000*(P|G 12%,8) 11 12 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 13 14 EOY CF 15 0 -$50,000.00 16 1 $13,000.00 17 2 $12,000.00 18 3 $11,000.00 19 4 $10,000.00 20 5 $9,000.00 21 6 $8,000.00 22 7 $7,000.00 23 8 $6,000.00 24 25 PW= $107.87 USING EXCEL'S NPV FUNCTION THIS IS 26 =NPV(12%,CF YR 1:CF YR 8)-50000

A B C D 1 PROBLEM 2.103 2 3 i= 10.00% 4 n= 8 5 INITIAL CF= -$50,000.00 A1= 6 $13,000.00 7 G= -$1,000.00 8 9 A= $623.52 USING INTEREST TABLES THIS IS 10 =-$50,000*(A|P 10%,8)+$13,000-$1,000*(A|G 10%,8) 11 12 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 13 14 EOY CF 15 0 -$50,000.00 16 1 $13,000.00 17 2 $12,000.00 18 3 $11,000.00 19 4 $10,000.00 20 5 $9,000.00 21 6 $8,000.00 22 7 $7,000.00 23 8 $6,000.00 24 25 A= $623.32 USING EXCEL'S PMT AND NPV FUNCTIONS THIS IS 26 =PMT(10%,8,-(NPV(10%,CF YR 1:CF YR 8)-50000))

E 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

A B C D E F G H I 1 PROBLEM 2.104 2 3 4 i= 8.00% 5 n= 8 6 INITIAL CF= -$50,000.00 A1= 7 $13,000.00 8 G= -$1,000.00 9 10 FW= $12,771.82 USING INTEREST TABLES THIS IS 11 =(-$50,000+$13,000*(P|A 8%,8)-$1,000*(P|G 8%,8))*(F|P 8%,8) 12 13 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 14 15 EOY CF 16 0 -$50,000.00 17 1 $13,000.00 18 2 $12,000.00 19 3 $11,000.00 20 4 $10,000.00 21 5 $9,000.00 22 6 $8,000.00 23 7 $7,000.00 24 8 $6,000.00 25 26 FW= $12,771.80 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS 27 =FV(8%,8,,-(NPV(8%,CF YR 1:CF YR 8)-50000))

A B C D E F G H I 1 PROBLEM 2.105 2 3 i= 6.00% 4 n= 8 5 INITIAL CF= -$50,000.00 A1= 6 $13,000.00 7 G= -$1,000.00 8 9 FIRST, DETERMINE THE PW OF THE CASH FLOW SERIES 10 PW= $10,885.69 USING INTEREST TABLES THIS IS 11 =-$50,000+$13,000*(P|A 6%,8)-$1,000*(P|G 6%,8) 12 NOW, DETERMINE THE VALUE OF X FOR THE EQUIVALENT SERIES X, 2X, 3X, …, 8X 13 PW= $10,885.69 =X*(P|A 6%,8)+X*(P|G 6%,8) 14 $10,885.69 =X*(6.20979+19.84158) 15 $10,885.69 =26.05137*X 16 X= $417.85 17 18 THIS CAN ALSO BE WELL APPROACHED USING SOLVER AS FOLLOWS 19 FIRST, DETERMINE THE PW OF THE ORIGINAL CASH FLOW SERIES. THEN, LET X BE ANY VALUE AND SET UP A TABLE OVER 8 YEARS ASSUMING THE VALUE OF X IS CORRECT. DETERMINE THE PW OF THE CASH FLOWS IN THE TABLE USING THE CELL WHERE YOUR VALUE OF X IS STORED. THEN, USE SOLVER TO DETERMINE THE VALUE OF X THAT MAKES THE PW OF THE CASH FLOWS EQUAL TO THE PW VALUE OF THE ORIGINAL CASH FLOW 20 SERIES 21 22 X= $417.86 <--SOLVER CHANGED CELL 23 24 EOY CF EOY CF 25 0 -$50,000.00 0 0 26 1 $13,000.00 1 $417.86 27 2 $12,000.00 2 $835.71 28 3 $11,000.00 3 $1,253.57 29 4 $10,000.00 4 $1,671.43 30 5 $9,000.00 5 $2,089.28 31 6 $8,000.00 6 $2,507.14 32 7 $7,000.00 7 $2,925.00 33 8 $6,000.00 8 $3,342.85 34 35 PW= $10,885.74 PW= $10,885.74 <--SOLVER TARGET CELL 36 USING EXCEL'S NPV FUNCTION USING EXCEL'S NPV FUNCTION 37 =NPV(6%,CF YR 1:CF YR 8)-50000 =NPV(6%,CF YR 1:CF YR 8)+0

A B C D E F G H 1 PROBLEM 2.106 2 3 i= 6.00% 4 n= 8 5 INITIAL CF= -$45,000.00 A1= 6 $12,000.00 7 G= -$1,000.00 8 9 PW= $9,675.90 USING INTEREST TABLES THIS IS 10 =-$45,000+$12,000*(P|A 6%,8)-$1,000*(P|G 6%,8) 11 AMT6= $13,725.46 USING INTEREST TABLES THIS IS 12 =$9,675.90*(F|P 6%,6) 13 14 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 15 16 EOY CF 17 0 -$45,000.00 18 1 $12,000.00 19 2 $11,000.00 20 3 $10,000.00 21 4 $9,000.00 22 5 $8,000.00 23 6 $7,000.00 24 7 $6,000.00 25 8 $5,000.00 26 27 PW= $9,675.95 USING EXCEL'S NPV FUNCTION THIS IS =NPV(6%,12000,11000,10000,9000,8000,7000,6000,50 28 00)-45000 29 AMT6= $13,725.51 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS =FV(6%,6,,(NPV(6%,12000,11000,10000,9000,8000,7000,6000,50 30 00)-45000))

A B C D 1 PROBLEM 2.107 2 3 i= 6.00% n1= 4 8 YEARS IN ORIGINAL GRADIENT SERIES 5 INITIAL CF= -$45,000.00 A1= 6 $12,000.00 7 G= -$1,000.00 8 t= 3 YEAR BEFORE ANNUAL SERIES FROM 4 TO 7 n2= 9 4 YEARS IN UNIFORM ANNUAL SERIES 10 11 PW= $9,675.90 USING INTEREST TABLES THIS IS 12 =-$45,000+$12,000*(P|A 6%,8)-$1,000*(P|G 6%,8) 13 AMT3= $11,524.19 USING INTEREST TABLES THIS IS 14 =$9,675.90*(F|P 6%,3) 15 A(4-7)= $3,325.77 USING INTEREST TABLES THIS IS 16 =$11,524.19*(A|P 6%,4) 17 18 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 19 20 EOY CF 21 0 -$45,000.00 22 1 $12,000.00 23 2 $11,000.00 24 3 $10,000.00 25 4 $9,000.00 26 5 $8,000.00 27 6 $7,000.00 28 7 $6,000.00 29 8 $5,000.00 30 31 PW= $9,675.95 USING EXCEL'S NPV FUNCTION THIS IS 32 =NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-45000 33 AMT3= $11,524.21 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS 34 =FV(6%,3,,-(NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-4500 35 A(4-7)= $3,325.79 USING EXCEL'S PMT FUNCTION THIS IS 36 =PMT(6%,4,-11524.21)

E F 1 2 3 YEARS IN 4 ORIGINAL GRADIENT SERIES 5 6 7 YEAR BEFORE 8 ANNUAL SERIES FROM 4 TO 7 YEARS IN 9 UNIFORM ANNUAL SERIES 10 USING INTEREST 11 TABLES THIS IS =-$45,000+$12,000*(P|A 12 6%,8)-$1,000*(P|G 6%,8) USING INTEREST 13 TABLES THIS IS =$9,675.90*(F|P 14 6%,3) USING INTEREST 15 TABLES THIS IS =$11,524.19*(A|P 16 6%,4) 17 BULATED CASH 18 FLOWS TO CHECK ANSWER 19 20 21 22 23 24 25 26 27 28 29 30 USING EXCEL'S 31 NPV FUNCTION THIS IS =NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-45000 32 USING EXCEL'S 33 FV AND NPV FUNCTIONS THIS IS =FV(6%,3,,-(NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-45000)) 34 USING EXCEL'S 35 PMT FUNCTION THIS IS =PMT(6%,4,-11524.21) 36

A B C D E F G H 1 PROBLEM 2.108 2 3 FROM PROBLEM 2.106: 4 i= 6.00% 5 n= 8 6 INITIAL CF= -$45,000.00 A1= 7 $12,000.00 8 G= -$1,000.00 9 PW= $9,675.90 USING INTEREST TABLES THIS IS 10 =-$45,000+$12,000*(P|A 6%,8)-$1,000*(P|G 6%,8) 11 NOW, SET UP A NEW GRADIENT SERIES THAT HAS THE SAME PW AS THE 12 ORIGINAL SERIES 13 14 PW= $9,675.90 USING INTEREST TABLES THIS IS =A1*(P|A 6%,8)+G*(P|G 6%,8) 15 A8= 16 WE KNOW $10,000 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

WE KNOW PW=

$10,000-7*G $9,675.90 =-$45,000+($10,000-7*G)*(P|A 6%,8)+G*(P|G 6%,8) =-$45,000+($10,000-7*G)*6.20979+G*19.84158 =$17,097.90-23.62695*G $314.13

THEREFORE A8=

$10,000.00 GIVEN IN PROBLEM

A1=

$7,801.07 =10000-7*314.13 $314.13

THIS IS EASIER DONE USING SOLVER AS FOLLOWS FIRST, FIND THE PW OF THE ORIGINAL GRADIENT SERIES EOY 0 1 2 3 4 5 6 7 8 PW=

44 45 46 47 48 49

A1=

CF -$45,000.00 $12,000.00 $11,000.00 $10,000.00 $9,000.00 $8,000.00 $7,000.00 $6,000.00 $5,000.00 $9,675.95 USING EXCEL'S NPV FUNCTION THIS IS =NPV(6%,12000,11000,10000,9000,8000,7000,6000,50 00)-45000

NOW, SET THE GRADIENT AMOUNT "G" TO ANY VALUE AND GO FORWARD AS IF IT IS THE CORRECT VALUE G=

$314.13 <--SOLVER CHANGED CELL

50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66

NOW, SET UP ANOTHER TABLE OF CASH FLOWS USING THE FACT THAT A8=$10,000, A1=$10,000-7*G, AND A0=-$45,000. THEN, USE SOLVER TO FIND THE PW OF THE SERIES EQUAL TO THAT OF THE ORIGINAL SERIES WHILE CHANGING THE VALUE OF G A8=

$10,000.00 GIVEN IN PROBLEM

EOY 0 1 2 3 4 5 6 7 8

CF -$45,000.00 $7,801.08 $8,115.21 $8,429.34 $8,743.47 $9,057.60 $9,371.74 $9,685.87 $10,000.00

PW=

$9,675.95 <--SOLVER TARGET CELL =NPV(6%,CF YR 1:CF YR 8)-45000

A 1 PROBLEM 2.109 2 3 4 5 6 7 8 a 9 10 11 12 13 b 14 15 16

i= n= A1=

8.00% 5 $500.00 $100.00

P= $2,733.60 USING INTEREST TABLES THIS IS =$500*(P|A 8%,5)+$100*(P|G 8%,5) P= $2,733.60 USING EXCEL'S NPV FUNCTION THIS IS =NPV(C3,500,600,700,800,900) A= A=

$684.65 USING INTEREST TABLES THIS IS =$500+$100*(A|G 8%,5) $684.65 USING EXCEL'S PMT FUNCTION THIS IS =PMT(8%,5,-2733.60)

A 1 PROBLEM 2.110 2 3 4 5 6 7 8 a 9 10 11 12 13 14 15 b 16 17 18 19 20

i= n= A1= G= P= F= F=

A= A= A=

12.00% 25 $1,000.00 $200.00 $18,464.07 USING INTEREST TABLES THIS IS =$1,000*(P|A 12%,25)+$200*(P|G 12%,25) $313,890.26 USING INTEREST TABLES THIS IS =$18,464.07*(F|P 12%,25) $313,890.35 USING EXCEL'S FV FUNCTION THIS IS =FV(12%,25,,-18464.07) $2,354.17 USING INTEREST TABLES THIS IS =$1,000+$200*(A|G 12%,25) $2,354.18 USING INTEREST TABLES THIS IS =$313,890.35*(A|F 12%,25) $2,354.17 USING EXCEL'S PMT FUNCTION THIS IS =PMT(12%,25,,-313890.35)

A 1 PROBLEM 2.111 2 3 4 5 6 7 8 a 9 10 11 12 13 14 15 b 16 17 18 19 20

i= n= A1=

10.00% 10 $7,000.00 -$300.00

$36,144.59 USING INTEREST TABLES THIS IS =$7,000*(P|A 10%,10)-$300*(P|G 10%,10) F= $93,749.66 USING INTEREST TABLES THIS IS =$36,144.59*(F|P 10%,10) F= $93,749.75 USING EXCEL'S FV FUNCTION THIS IS =FV(10%,10,,-36144.59)

A= A= A=

$2,354.17 USING INTEREST TABLES THIS IS =$7,000-$300*(A|G 10%,10) $5,882.80 USING INTEREST TABLES THIS IS =$93,749.66*(A|F 10%,10) $5,882.37 USING EXCEL'S PMT FUNCTION THIS IS =PMT(10%,10,,-93749.75)

A B C D E F G 1 PROBLEM 2.112 2 3 i= 8.00% 4 n= 6 5 P= $140,000.00 A1= 6 $11,000.00 7 X= G 8 a THE PAYMENTS MUST HAVE A PW EQUAL TO THE COST OF THE MACHINERY. SINCE THE FIRST PAYMENT IS KNOWN, SOLVE FOR THE 9 GRADIENT PAYMENT G. 10 11 PW= USING INTEREST TABLES THIS IS 12 =$11,000*(P|A 8%,6)+G*(P|G 8%,6) 13 =$11,000*4.62288+G*10.52327 14 SO $140,000.00 =$50,851.68+G*10.52327 15 G=X $8,471.54 =(140000-50851.68)/10.52327 16

17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

40 41 42

THIS MAY ALSO BE APPROACHED USING SOLVER. BEGIN BY SETTING THE VALUE OF "G" TO ANY VALUE. IT WILL LATER BE CHANGED TO THE CORRECT VALUE. THEN USE THE EXCEL CELL WITH THAT VALUE OF G TO DEVELOP A CASH FLOW SERIES. WRITE AN EQUATION FOR THE PW OF THE SERIES. THEN, USE SOLVER TO TARGET THE PW TO THE COST OF THE MACHINERY BY CHANGING THE VALUE OF G. G=X EOY 0 1 2 3 4 5 6 P=

LAST PAYMENT

i= n= P= G=X

CF $11,000.00 $19,471.54 $27,943.08 $36,414.62 $44,886.16 $53,357.69 $140,000.00 <--SOLVER TARGET CELL =NPV(8%,CF YR 1:CF YR 6)+0 $53,357.69 =11000+5*8471.54 8.00% 6 $140,000.00 -$7,500.00

THE PAYMENTS MUST HAVE A PW EQUAL TO THE COST OF THE MACHINERY. SINCE THE GRADIENT IS KNOWN, SOLVE FOR THE FIRST PAYMENT A1. PW= $140,000.00 USING INTEREST TABLES THIS IS $140,000.00 =A1*(P|A 8%,6)-$7,500*(P|G 8%,6)

43 44

$8,471.54 <--SOLVER CHANGED CELL

SO A1=

$140,000.00 =A1*4.62288-$7,500*10.52327 $140,000.00 =A1*4.62288-$78,924.53 $47,356.74 =(140000+78924.53)/4.62288

47 48 49 50 51 52 53 54 55 56 57 58 59 60 61

THIS MAY ALSO BE APPROACHED USING SOLVER. BEGIN BY SETTING THE VALUE OF "A1" TO ANY VALUE. IT WILL LATER BE CHANGED TO THE CORRECT VALUE. THEN USE THE EXCEL CELL WITH THAT VALUE OF A1 TO DEVELOP A CASH FLOW SERIES. WRITE AN EQUATION FOR THE PW OF THE SERIES. THEN, USE SOLVER TO TARGET THE PW TO THE COST OF THE MACHINERY BY CHANGING THE VALUE OF A1. A1= EOY 0 1 2 3 4 5 6 P=

$47,356.75 <--SOLVER CHANGED CELL CF $47,356.75 $39,856.75 $32,356.75 $24,856.75 $17,356.75 $9,856.75 $140,000.00 <--SOLVER TARGET CELL =NPV(8%,CF YR 1:CF YR 6)+0

1 2 3 4 5 6 7 8 9

A PROBLEM 2.113

i= n= P= A= A1= X= a

10 11 12 13 14 15 16 17

18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

10.00% 9 $170,000.00 $10,000.00 YEARS 1, 2, 3, 4 $11,000.00 YEAR 5 G

THE PAYMENTS MUST HAVE A PW EQUAL TO THE COST OF THE MACHINERY. SINCE THE FIRST PAYMENT IS KNOWN, SOLVE FOR THE GRADIENT PAYMENT G. PW=

USING INTEREST TABLES THIS IS =$10,000*(P|A 10%,9)+G*(P|G 10%,6)*(P|F 10%,3) =$10,000*5.75902+G*9.68417*0.75131 SO $170,000.00 =$57590.20+G*7.27581 G=X= $15,449.80 $15,449.80 THIS MAY ALSO BE APPROACHED USING SOLVER. BEGIN BY SETTING THE VALUE OF "G" TO ANY VALUE. IT WILL LATER BE CHANGED TO THE CORRECT VALUE. THEN USE THE EXCEL CELL WITH THAT VALUE OF G TO DEVELOP A CASH FLOW SERIES. WRITE AN EQUATION FOR THE PW OF THE SERIES. THEN, USE SOLVER TO TARGET THE PW TO THE COST OF THE MACHINERY BY CHANGING THE VALUE OF G. G=X= EOY 0 1 2 3 4 5 6 7 8 9 P=

$15,449.68 <--SOLVER CHANGED CELL CF $10,000.00 $10,000.00 $10,000.00 $10,000.00 $25,449.68 $40,899.37 $56,349.05 $71,798.74 $87,248.42 $170,000.00 <--SOLVER TARGET CELL =NPV(10%,CF YR 1:CF YR 9)+0

b LAST PAYMENT= $87,248.42 =10000+5*15449.68 c

TOTAL INTEREST PAID= $151,745.27 =SUM(CF YR 0:CF YR 9)-170000

A B C D E F G H 1 PROBLEM 2.114 2 3 i= 10.00% 4 n= 5 A = 5 $10,000.00 1 6 G= -$1,000.00 7 8 P= $31,046.10 USING INTEREST TABLES THIS IS 9 =$10,000*(P|A 10%,5)-$1,000*(P|G 10%,5) 10 AMT3= $41,322.36 USING INTEREST TABLES THIS IS 11 $31,046.10*(F|P 10%,3) 12 13 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 14 15 EOY CF 16 0 $0.00 17 1 $10,000.00 18 2 $9,000.00 19 3 $8,000.00 20 4 $7,000.00 21 5 $6,000.00 22 23 AMT3= $41,322.31 USING EXCEL'S NPV AND FV FUNCTIONS THIS IS =NPV(10%,7000,6000)+FV(10%,2,,-10000)+FV(10%,1,,24 9000)+8000

A 1 PROBLEM 2.115 2 3 a 4 5 6 7

n= A0=

4 -$10,000.00

A1=

$3,000.00 $1,000.00

THIS PROBLEM, IN WHICH THE VALUE OF THE INTEREST RATE IS TO BE FOUND, IS BEST APPROACHED USING SOLVER. THIS IS DUE TO THE DIFFICULTY OF TRYING TO SOLVE ANALYTICALLY FOR THE INTEREST RATE USING FORMULAS OR INTERPOLATION. BEGIN BY SETTING A CELL TO HOUSE THE INTEREST RATE. SELECT ANY INTEREST RATE FOR THE VALUE IN THE CELL. IT WILL LATER BE SET TO THE CORRECT VALUE.

10 11 12 13

24.8883% <--SOLVER CHANGED CELL

NOW, DEVELOP A FORMULA FOR THE OVERALL PW AS A FUNCTION OF THE INTEREST RATE. THEN, USE SOLVER TO SET THE PW VALUE EQUAL TO 0 BY CHANGING THE INTEREST RATE i.

14 15 16 17 18 19

37 38 39 40 41 42 43 44

8 9

20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

PW=

$0.00 <--SOLVER TARGET CELL USING COMPOUND INTEREST FORMULAS THIS IS =-10000+3000*((1+i)^4-1)/(i*(1+i)^4)+1000*(1-(1+4*i)*(1+i)^(-4))/(i^2)

SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. NOTE THAT THE INTEREST RATE FOUND USING SOLVER BELOW IS THE SAME VALUE FOUND ABOVE. i=

24.8883% <--SOLVER CHANGED CELL

EOY CF 0 -$10,000.00 1 $3,000.00 2 $4,000.00 3 $5,000.00 4 $6,000.00 P=

$0.00 <--SOLVER TARGET CELL USING EXCEL'S NPV FUNCTION THIS IS =NPV(i%,3000,4000,5000,6000)-10000 24.8883%

BEGIN BY SETTING A CELL TO HOUSE THE VALUE OF THE EQUAL ANNUAL INCOMES, "A." SELECT ANY VALUE FOR "A" IN THE CELL. IT WILL LATER BE SET TO THE CORRECT VALUE. A= P=

$4,226.00 <--SOLVER CHANGED CELL $0.00 <--SOLVER TARGET CELL FORMULAS =-10000+A*((1+0.2489)^4-1)/(0.2489*(1+0.2489)^4)

45 46 47 48 49 50 51 52 53 54 55 56 57 58

B C D E F G H SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. NOTE THAT THE EQUAL ANNUAL INCOME "A" FOUND BELOW IS THE SAME VALUE FOUND ABOVE. A=

$4,226.00 <--SOLVER CHANGED CELL

EOY CF 0 -$10,000.00 1 $4,226.00 2 $4,226.00 3 $4,226.00 4 $4,226.00 P=

$0.00 <--SOLVER TARGET CELL USING EXCEL'S NPV FUNCTION THIS IS =NPV(24.8883%,4226,4226,4226,4226)-10000

A B C D E F G 1 PROBLEM 2.116 2 3 a P= INR 20,000,000.00 4 i= 5.00% 5 n= 10 A1= 6 INR 2,000,000.00 7 X= G 8 9 P= INR 20,000,000.00 USING INTEREST TABLES THIS IS 10 INR 20,000,000.00 =INR 2,000,000*(P|A 5%,10)+G*(P|G 5%,10) 11 INR 20,000,000.00 =INR 2,000,000*7.72173+G*31.65205 12 INR 20,000,000.00 =INR 15,443,460+G*31.65205 13 G=X= INR 143,957.18 =(20000000-15443460)/31.65205 14 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. NOTE THAT THE VALUE OF G=X FOUND USING SOLVER BELOW IS 15 ESSENTIALLY THE SAME VALUE FOUND ABOVE. 16 17 G=X= INR 143,956.88 <--SOLVER CHANGED CELL 18 19 EOY CF 20 0 INR 0.00 21 1 INR 2,000,000.00 22 2 INR 2,143,956.88 23 3 INR 2,287,913.77 24 4 INR 2,431,870.65 25 5 INR 2,575,827.53 26 6 INR 2,719,784.41 27 7 INR 2,863,741.30 28 8 INR 3,007,698.18 29 9 INR 3,151,655.06 30 10 INR 3,295,611.94 31 32 P= INR 20,000,000.00 <--SOLVER TARGET CELL 33 USING EXCEL'S NPV FUNCTION THIS IS 34 =NPV(5%,CF YR 1:CF YR 10)+0 35 36 b AMT5= INR 12,960,976.54 USING INTEREST TABLES THIS IS =INR 20,000,000*(F|P 5%,5)-2,000,000(F|A 37 5%,5)-143,957.18(P|G 5%,5)(F|P 5%,5) 38 AMT5= INR 12,961,013.55 USING INTEREST TABLES THIS IS =INR 2,719,784.41*(P|A 5%,5)+INR 39 143,956.88*(P|G 5%,5) 40 AMT5= INR 12,961,004.03 USING EXCEL'S NPV FUNCTION THIS IS 41 =NPV(5%,CF YR 6:CF YR 10)

A B C D E F G H I J K L M N O 1 PROBLEM 2.117 2 3 i= 7.00% 4 5 EOY -1 0 1 2 3 4 5 6 7 8 9 10 6 CF $1,200 $1,000 $800 $500 $500 $500 $500 $0 -$800 -$800 $0 $1,500 7 8 9 10 11 12 TO FIND THE VALUE OF AMT5, 13 14 AMT5= $6,189.74 USING INTEREST TABLES THIS IS =(($1,200-$200*(A|G 7%,3))*(F|A 7%,3)*(P|F 7%,2)+$500*(P|A 7%,4)*(P|F 7%,2)-$800*(F|A 7%,2)*(P|F 7%,9)+$1,500*(P|F 15 7%,11))*(F|P 7%,6) 16 17 CHECK THIS USING EXCEL'S NPV AND FV FUNCTIONS 18 19 AMT5= $6,189.73 USING EXCEL'S NPV AND FV FUNCTIONS THIS IS 20 =NPV(7%,CF YR 6:CF YR 10)+FV(7%,7,,-NPV(7%,CF YR -1:CF YR 5))

A 1 PROBLEM 2.118 2 3 4 5

i= n= A11=

8.00% 40 $2,000.00

G1=

$1,000.00

n1=

A12=

$21,000.00

G2=

-$1,000.00

10 11 12 13 14

n2=

30 31 32 33 34 35

36 37 38 39 40 41

42 43

FIRST, FIND THE PW OF THE CASH FLOW PROFILE. P=

15 16

17 18 19 20 21 22 23 24 25 26 27 28 29

$118,139.04 USING INTEREST TABLES THIS IS =$2,000*(P|A 8%,20)+$1,000*(P|G 8%,20)+($21,000*(P|A 8%,20)-$1,000*(P|G 8%,20))*(P|F 8%,20)

NOW, LET X EQUAL THE FIRST OF 40 AMOUNTS IN A GRADIENT SERIES WITH GRADIENT G=$500. SOLVE FOR THE PW OF THIS GRADIENT SERIES. G= P=

$500.00 $118,139.04 USING INTEREST TABLES THIS IS $118,139.04 =X*(P|A 8%,40)+$500*(P|G 8%,40) $118,139.04 =X*11.92461+$500*126.04220 $118,139.04 =11.92461*X+$63,021.10

X= $4,622.20 =(118139.04-63021.1)/11.92461 ********** OR, RATHER THAN PERFORM THE ABOVE CALCULATIONS, CAN USE SOLVER BEGIN BY SETTING A CELL TO HOUSE THE VALUE OF THE FIRST AMOUNT, X. SELECT ANY AMOUNT FOR THE VALUE IN THE CELL. IT WILL LATER BE SET TO THE CORRECT VALUE. X= G=

$4,622.20 <--SOLVER CHANGED CELL $500.00

NOW, DEVELOP A FORMULA FOR THE PW AS A FUNCTION OF X. THEN, USE SOLVER TO SET THE PW VALUE TO ITS TARGET VALUE BY CHANGING THE VALUE OF X. P=

$118,139.04 <--SOLVER TARGET CELL USING INTEREST TABLES THIS IS =X*(P|A 8%,40)+$500*(P|G 8%,40)

********** SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. NOTE THAT THE VALUE OF X FOUND USING SOLVER BELOW IS ESSENTIALLY THE SAME VALUE FOUND ABOVE. BEGIN BY SETTING A CELL TO HOUSE THE VALUE OF THE FIRST AMOUNT, X. SELECT ANY AMOUNT FOR THE VALUE IN THE CELL. IT WILL LATER BE SET TO THE CORRECT VALUE.

A 45 46 47

48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96

B X=

$4,622.18 <--SOLVER CHANGED CELL

FIRST SOLVE FOR THE PW OF THE ORIGINAL GRADIENT SERIES. THEN, ADJUST THE PW OF THE NEW GRADIENT SERIES WITH FIRST AMOUNT X AND GRADIENT G=500 TO THE PW OF THE ORIGINAL SERIES BY ADJUSTING THE VALUE OF X. NOTE THAT THE VALUE OF X BELOW IS ESSENTIALLY THE SAME AS THE VALUE FOUND ABOVE.

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 P=

ORIGINAL CF $0.00 $2,000.00 $3,000.00 $4,000.00 $5,000.00 $6,000.00 $7,000.00 $8,000.00 $9,000.00 $10,000.00 $11,000.00 $12,000.00 $13,000.00 $14,000.00 $15,000.00 $16,000.00 $17,000.00 $18,000.00 $19,000.00 $20,000.00 $21,000.00 $21,000.00 $20,000.00 $19,000.00 $18,000.00 $17,000.00 $16,000.00 $15,000.00 $14,000.00 $13,000.00 $12,000.00 $11,000.00 $10,000.00 $9,000.00 $8,000.00 $7,000.00 $6,000.00 $5,000.00 $4,000.00 $3,000.00 $2,000.00

NEW CF $0.00 $4,622.18 $5,122.18 $5,622.18 $6,122.18 $6,622.18 $7,122.18 $7,622.18 $8,122.18 $8,622.18 $9,122.18 $9,622.18 $10,122.18 $10,622.18 $11,122.18 $11,622.18 $12,122.18 $12,622.18 $13,122.18 $13,622.18 $14,122.18 $14,622.18 $15,122.18 $15,622.18 $16,122.18 $16,622.18 $17,122.18 $17,622.18 $18,122.18 $18,622.18 $19,122.18 $19,622.18 $20,122.18 $20,622.18 $21,122.18 $21,622.18 $22,122.18 $22,622.18 $23,122.18 $23,622.18 $24,122.18

$118,138.78 $118,138.78 <--SOLVER TARGET CELL USING EXCEL'S NPV FUNCTION THIS IS =NPV(8%,NEW CF YR 1: NEW CF YR 40)+CF YR 0

A B 1 PROBLEM 2.119 2 3 EOY 4 CF 5 6 i= 7 n= A1= 8 9 G= 10 11 PW= 12 13 14 PW= 15

0 $100

2 3 4 5 6 7 8 9 10 $80 $60 $40 $20 $0 -$20 -$40 -$60 -$80 -$100

18.00% 11 $ 100.00 -$20.00 $ 172.48 USING INTEREST TABLES THIS IS =($100*(P|A 18%,11)-$20*(P|G 18%,11))*(F|P18%,1) $172.48 USING EXCEL'S FV FUNCTION THIS IS =FV(18%,1,,-NPV(18%,100,80,60,40,20,0,-20,-40,-60,-80,-100))

A 1 PROBLEM 2.120 2 3 4 5 6 7 8 9 10 11 12

TOTAL EOY CF1 CF2 CF3 CF4 CF 0 $800.00 $800.00 1 $950.00 $0.00 $950.00 2 $950.00 -$450.00 $500.00 3 $950.00 -$900.00 $50.00 4 $950.00 -$1,350.00 -$400.00 5 -$600.00 -$600.00 6 -$600.00 -$600.00 7 -$600.00 -$600.00

A 1 PROBLEM 2.121 2 3 4 5 6 7 8 9 10 11 12 13 14

EOY CF1 CF2 CF3 CF 0 -$7,000.00 -$7,000.00 1 $0.00 2 $0.00 3 $0.00 4 $0.00 5 $1,850.00 $0.00 $1,850.00 6 $1,850.00 $200.00 $2,050.00 7 $1,850.00 $400.00 $2,250.00 8 $1,850.00 $600.00 $2,450.00 9 $1,850.00 $800.00 $2,650.00 10 $1,850.00 $1,000.00 $2,850.00

A B C D E F G H I 1 PROBLEM 2.123 2 P|A1 FACTOR 3 4 5 i= USING 7.00%7% FOR EXAMPLE CALC 6 j= USING 5.00%5% FOR EXAMPLE CALC 7 n= USING 10 10 FOR EXAMPLE CALC P|A = 8 CHECKS WITH GEOMETRIC 8.59763 SERIES-PRESENT WORTH TABLE 1 9 10 F|A1 FACTOR 11 12 13 i= 7.00% USING 7% FOR EXAMPLE CALC 14 j= 5.00% USING 5% FOR EXAMPLE CALC 15 n= 10 USING 10 FOR EXAMPLE CALC F|A1= 16.91284 CHECKS WITH GEOMETRIC SERIES-FUTURE WORTH TABLE 16 17 18 A|A1 FACTOR 19 20 21 i= 7.00% USING 7% FOR EXAMPLE CALC 22 j= 5.00% USING 5% FOR EXAMPLE CALC 23 n= 10 USING 10 FOR EXAMPLE CALC A|A1= 1.22411 NOT TABULATED IN APPENDIX A 24 25 26 NOW, COMPLETING THE PROBLEM: 27 A1= $1,000.00 28 29 i= 7.00% 30 j= 5.00% 31 32 A= $1,224.11 USING A|A1 FACTOR 33 34 35 36 37 38 39 40 41

=$1,000*1.22411 A=

$1,224.13 USING P|A1 FACTOR * A|P FACTOR =$1,000*(P|A1 7%,5%,10)*(A|P 7%,10) =$1,000*8.59763*0.14238

$1,224.15 USING F|A1 FACTOR * A|F FACTOR =$1,000*(F|A1 7%,5%,10)*(A|F 7%,10) =$1,000*16.91284*0.07238

A B C D E F G 1 PROBLEM 2.124 2 3 i= 5.00% 4 n= 30 A = 5 $7,500.00 1 6 j= 5.00% 7 8 F= $926,130.53 USING INTEREST TABLES THIS IS =$7,500*(F|A1 5%,5%,30) 9 10 ********** 11 12 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 13 14 EOY CF 15 0 16 1 $7,500.00 =$7,500*(1+0.05)^(1-1) 17 2 $7,875.00 =$7,500*(1+0.05)^(2-1) 18 3 $8,268.75 19 4 $8,682.19 20 5 $9,116.30 21 6 $9,572.11 22 7 $10,050.72 23 8 $10,553.25 24 9 $11,080.92 25 10 $11,634.96 26 11 $12,216.71 27 12 $12,827.55 28 13 $13,468.92 29 14 $14,142.37 30 15 $14,849.49 31 16 $15,591.96 32 17 $16,371.56 33 18 $17,190.14 34 19 $18,049.64 35 20 $18,952.13 36 21 $19,899.73 37 22 $20,894.72 38 23 $21,939.46 39 24 $23,036.43 40 25 $24,188.25 41 26 $25,397.66 42 27 $26,667.55 43 28 $28,000.92 44 29 $29,400.97 45 30 $30,871.02 =$7,500*(1+0.05)^(30-1) 46 47 F= $926,130.51 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS 48 =FV(5%,30,,-NPV(5%,CF YR 1:CF YR 30)+0)

A B C D E F G 1 PROBLEM 2.125 2 3 i= 6.00% 4 n= 30 A = 5 $7,500.00 1 6 j= 6.00% 7 8 F= $1,219,137.30 USING INTEREST TABLES THIS IS =$7,500*(F|A1 6%,6%,30) 9 10 ********** 11 12 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 13 14 EOY CF 15 0 16 1 $7,500.00 =$7,500*(1+0.06)^(1-1) 17 2 $7,950.00 =$7,500*(1+0.06)^(2-1) 18 3 $8,427.00 19 4 $8,932.62 20 5 $9,468.58 21 6 $10,036.69 22 7 $10,638.89 23 8 $11,277.23 24 9 $11,953.86 25 10 $12,671.09 26 11 $13,431.36 27 12 $14,237.24 28 13 $15,091.47 29 14 $15,996.96 30 15 $16,956.78 31 16 $17,974.19 32 17 $19,052.64 33 18 $20,195.80 34 19 $21,407.54 35 20 $22,692.00 36 21 $24,053.52 37 22 $25,496.73 38 23 $27,026.53 39 24 $28,648.12 40 25 $30,367.01 41 26 $32,189.03 42 27 $34,120.37 43 28 $36,167.59 44 29 $38,337.65 45 30 $40,637.91 =$7,500*(1+0.06)^(30-1) 46 47 F= $1,219,137.28 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS 48 =FV(6%,30,,-NPV(6%,CF YR 1:CF YR 30)+0)

A B C D E F 1 PROBLEM 2.126 2 3 i= 5.00% 4 n= 35 A = 5 $7,500.00 1 6 j= 8.00% 7 8 F= $2,317,332.23 USING ELECTRONIC INTEREST TABLES THIS IS =$7,500*(F|A1 5%,8%,35) 9 10 ********** 11 12 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER 13 14 AGE EOY CF 15 25 0 16 26 1 $7,500.00 =$7,500*(1+0.08)^(1-1) 17 27 2 $8,100.00 =$7,500*(1+0.08)^(2-1) 18 28 3 $8,748.00 19 29 4 $9,447.84 20 30 5 $10,203.67 21 31 6 $11,019.96 22 32 7 $11,901.56 23 33 8 $12,853.68 24 34 9 $13,881.98 25 35 10 $14,992.53 26 36 11 $16,191.94 27 37 12 $17,487.29 28 38 13 $18,886.28 29 39 14 $20,397.18 30 40 15 $22,028.95 31 41 16 $23,791.27 32 42 17 $25,694.57 33 43 18 $27,750.14 34 44 19 $29,970.15 35 45 20 $32,367.76 36 46 21 $34,957.18 37 47 22 $37,753.75 38 48 23 $40,774.05 39 49 24 $44,035.98 40 50 25 $47,558.86 41 51 26 $51,363.56 42 52 27 $55,472.65 43 53 28 $59,910.46 44 54 29 $64,703.30 45 55 30 $69,879.56 46 56 31 $75,469.93 47 57 32 $81,507.52 48 58 33 $88,028.12 49 59 34 $95,070.37 50 60 35 $102,676.00 =$7,500*(1+0.08)^(35-1) 51 F= $2,317,332.23 USING EXCEL'S FV AND NPV 52 FUNCTIONS THIS IS =FV(8%,35,,-NPV(8%,CF YR 1:CF 53 YR 35)+0)

PROBLEM 2.127 FIRST, REVIEW THE ORIGINAL PROBLEM 2.126 i= n= A1= j= F=

5.00% 35 $7,500.00 8.00% $2,317,332.23 USING ELECTRONIC INTEREST TABLES THIS IS =$7,500*(F|A1 5%,8%,35)

NOW, SOLVE FOR THE FIRST INVESTMENT ON HIS 36TH BIRTHDAY TO ACHIEVE THE SAME VALUE OF FW AT EOY 60. LET A1 BE THE VALUE OF THE FIRST INVESTMENT AT EOY 36. F=

$2,317,332.23 USING ELECTRONIC INTEREST TABLES THIS IS $2,317,332.23 =A1*(F|A1 5%,8%,25) $2,317,332.23 =A1*115.401008511

A1= $20,080.69 =2317332.23/115.401008511 ********** SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. NOTE THAT THE VALUE OF A1 FOUND USING SOLVER BELOW IS ESSENTIALLY THE SAME VALUE FOUND ABOVE. A1= AGE 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

$20,080.17 SOLVER CHANGED CELL ORIGINAL EOY CF 0 1 $7,500.00 =$7,500*(1+0.08)^(1-1) 2 $8,100.00 =$7,500*(1+0.08)^(2-1) 3 $8,748.00 4 $9,447.84 5 $10,203.67 6 $11,019.96 7 $11,901.56 8 $12,853.68 9 $13,881.98 10 $14,992.53 11 $16,191.94 12 $17,487.29 13 $18,886.28 14 $20,397.18 15 $22,028.95 16 $23,791.27 17 $25,694.57 18 $27,750.14 19 $29,970.15 20 $32,367.76 21 $34,957.18 22 $37,753.75 23 $40,774.05 24 $44,035.98 25 $47,558.86 26 $51,363.56

AGE EOY 25 0 26 1 27 2 28 3 29 4 30 5 31 6 32 7 33 8 34 9 35 10 36 11 37 12 38 13 39 14 40 15 41 16 42 17 43 18 44 19 45 20 46 21 47 22 48 23 49 24 50 25 51 26

NEW CF $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $0.00 $20,080.17 $21,686.58 $23,421.51 $25,295.23 $27,318.85 $29,504.36 $31,864.71 $34,413.88 $37,167.00 $40,140.35 $43,351.58 $46,819.71 $50,565.29 $54,610.51 $58,979.35 $63,697.70

52 53 54 55 56 57 58 59 60

27 28 29 30 31 32 33 34 35 F=

$55,472.65 $59,910.46 $64,703.30 $69,879.56 $75,469.93 $81,507.52 $88,028.12 $95,070.37 $102,676.00 =$7,500*(1+0.08)^(35-1) $2,317,332.23

USING EXCEL'S FV AND NPV FUNCTIONS THIS IS =FV(8%,35,,-NPV(8%,CF YR 1:CF YR 35)+0)

52 53 54 55 56 57 58 59 60

27 28 29 30 31 32 33 34 35

$68,793.51 $74,297.00 $80,240.76 $86,660.02 $93,592.82 $101,080.24 $109,166.66 $117,899.99 $127,331.99

$2,317,332.23

SOLVER TARGET CELL USING EXCEL'S FV AND NPV FUNCTIONS THIS IS =FV(8%,35,,NPV(8%,CF YR 1:CF YR 35)+0)

A B C D E F G H 1 PROBLEM 2.128 2 3 FIRST, REVIEW THE ORIGINAL PROBLEM 2.126 4 5 i= 5.00% 6 j= 8.00% 7 n= 35 A1= 8 $7,500.00 9 10 F= $2,317,332.23 USING ELECTRONIC INTEREST TABLES THIS IS =$7,500*(F|A1 5%,8%,35) 11 12 NOW, SOLVE FOR THE UNIFORM ANNUAL INVESTMENT TO ACHIEVE THE SAME VALUE OF FW AT EOY 60. LET A BE THE 13 VALUE OF THE ANNUAL INVESTMENT. 14 15 F= $2,317,332.23 USING COMPOUND INTEREST FORMULAS THIS IS 16 =7500*(((1+0.05)^35-(1+0.08)^35))/(0.05-0.08) 17 18 A= $25,656.82 USING COMPOUND INTEREST FORMULAS THIS IS 19 =2317332.23*(0.05/((1+0.05)^35-1)) 20 21 A= $25,652.87 USING INTEREST TABLES THIS IS 22 =$2,317,332.23*(A|F 5%,35) 23 24 A= $25,656.82 USING EXCEL'S PMT FUNCTION THIS IS 25 =PMT(5%,35,,-2317332.23) 26

27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. NOTE THAT THE VALUE OF "A" FOUND USING SOLVER BELOW IS ESSENTIALLY THE SAME VALUE FOUND ABOVE. A=

$25,656.82

AGE 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43

EOY 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

ORIGINAL CF

CHECK AGE EOY 25 0 $7,500.00 26 1 $8,100.00 27 2 $8,748.00 28 3 $9,447.84 29 4 $10,203.67 30 5 $11,019.96 31 6 $11,901.56 32 7 $12,853.68 33 8 $13,881.98 34 9 $14,992.53 35 10 $16,191.94 36 11 $17,487.29 37 12 $18,886.28 38 13 $20,397.18 39 14 $22,028.95 40 15 $23,791.27 41 16 $25,694.57 42 17 $27,750.14 43 18

NEW CF $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82

A 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73

B 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

C 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

D $29,970.15 $32,367.76 $34,957.18 $37,753.75 $40,774.05 $44,035.98 $47,558.86 $51,363.56 $55,472.65 $59,910.46 $64,703.30 $69,879.56 $75,469.93 $81,507.52 $88,028.12 $95,070.37 $102,676.00

$2,317,332.23

USING EXCEL'S FV AND NPV =FV(8%,35,,-NPV(8%,CF YR 1:CF YR 35)+CF YR 0)

E 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

F 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

G $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82 $25,656.82

$2,317,332.23 SOLVER TARGET CELL USING EXCEL'S FV =FV(8%,35,,NPV(8%,CF YR 1:CF YR 35)+CF YR 0)

1 2 3 4 5 6 7 8 9 10 11 12

13 14 15 16 17 18 19 20 21 22 23 24 25 26

27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

EXCEL

A B C D E F 1 PROBLEM 2.129 2 3 P= -$90,000.00 4 i= 5.00% 5 j= -10.00% 6 n= 5 A1= 7 $30,000.00 8 9 PW= $17,467.13 USING COMPOUND INTEREST FORMULAS THIS IS 10 =30000*((1-(1-0.1)^5*(1+0.05)^-5)/(0.05+0.1))-90000 11 12 PW= $17,467.20 USING INTEREST TABLES THIS IS =$30,000*(P|A1 5%,-10%,5)-$90,000 13 14 15 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. 16 17 EOY CF 18 0 -$90,000.00 19 1 $30,000.00 20 2 $27,000.00 21 3 $24,300.00 22 4 $21,870.00 23 5 $19,683.00 24 25 PW= $17,467.13 USING EXCEL'S NPV FUNCTION THIS IS 26 =NPV(5%,CF YR 1:CF YR 5)-90000

A B C D E F G H 1 PROBLEM 2.130 2 3 FIRST, FIND THE PW OF THE GIVEN CF PROFILE 4 5 i= 6.00% 6 n= 8 7 INIT INV= $45,000.00 A1= 8 $12,000.00 9 G= -$1,000.00 10 11 P= $9,675.90 USING INTEREST TABLES THIS IS 12 -$45,000+$12,000(P|A 6%,8)-$1,000(P|G 6%,8) 13 14 P= $9,675.95 USING EXCEL'S NPV FUNCTION THIS IS =NPV(6%,12000,11000,10000,9000,8000,7000,6000,50 15 00)-45000 16 17 AT THIS POINT, WE KNOW THE PW OF THE CF PROFILE. 18 TO SOLVE FOR THE VALUE OF j, IT IS MUCH EASIER TO USE SOLVER 19 RATHER THAN TO TRY INTERPOLATION OR AN ANALYTICAL SOLUTION 20 21 i= 6.00% 22 n= 8 23 INIT INV= $45,000 A1= 24 $10,000 25

26 27 28 29 30 31 32 33

34 35 36 37 38 39 40 41 42 43 44 45 46 47

BEGIN BY SETTING THE VALUE OF "j" TO ANY VALUE. IT WILL LATER BE CHANGED TO THE CORRECT VALUE. THEN USE THE EXCEL CELL WITH THAT VALUE OF j TO DEVELOP THE CASH FLOW SERIES. WRITE AN EQUATION FOR THE PW OF THE SERIES. THEN, USE SOLVER TO TARGET THE PW TO EQUAL THE PW OF THE ORIGINAL CF SERIES BY CHANGING j. j= P=

-4.04% <--SOLVER CHANGED CELL $9,675.90 <--SOLVER TARGET CELL USING INTEREST TABLES THIS IS -$45,000+$10,000*(P|A1 6%,j%,8)

SEE BELOW FOR TABULATED CASH FLOWS WITH SOLVER USED TO CONFIRM THE ABOVE ANSWER. NOTE THAT THE VALUE OF j FOUND IS EQUAL TO THAT FOUND ABOVE. j= EOY 0 1 2 3 4 5 6 7 8

-4.04% <--SOLVER CHANGED CELL CF -$45,000.00 $10,000.00 $9,596.29 $9,208.87 $8,837.10 $8,480.33 $8,137.97 $7,809.43 $7,494.15

A 48 49 50 51

B PW=

$9,675.95 <--SOLVER TARGET CELL USING EXCEL'S NPV FUNCTION THIS IS =NPV(6%,CF YR 1:CF YR 8)-45000

A B C D E F G 1 PROBLEM 2.131 2 3 i= 5.00% 4 j= 10.00% 5 n= 18 A1= 6 $2,000.00 7 8 PW= $52,410.42 USING COMPOUND INTEREST FORMULA THIS IS =$2,000*(P|A1 5%,10%,18) 9 10 11 PW= $52,410.42 USING INTEREST TABLES THIS IS =$2,000*(P|A1 5%,10%,18) 12 13 14 FW= $126,131.92 USING EXCEL'S FV FUNCTION THIS IS 15 =FV(5%,18,,-52410.42) 16 17 SEE BELOW FOR TABULATED CASH FLOWS TO CONFIRM THE ANSWER. 18 19 EOY CF 20 0 21 1 $2,000.00 22 2 $2,200.00 23 3 $2,420.00 24 4 $2,662.00 25 5 $2,928.20 26 6 $3,221.02 27 7 $3,543.12 28 8 $3,897.43 29 9 $4,287.18 30 10 $4,715.90 31 11 $5,187.48 32 12 $5,706.23 33 13 $6,276.86 34 14 $6,904.54 35 15 $7,595.00 36 16 $8,354.50 37 17 $9,189.95 38 18 $10,108.94 39 40 PW= $52,410.42 USING EXCEL'S NPV FUNCTION THIS IS 41 =NPV(5%,CF YR 1:CF YR 18)+0 42 43 FW= $126,131.96 USING INTEREST TABLES THIS IS 44 =$52,410*(F|P 5%,18)

A B C D E F G 1 PROBLEM 2.132 2 3 i= 12.00% 4 j= 15.00% 5 n= 6 A1= 6 $50,000.00 7 8 PW= $286,447.62 USING COMPOUND INTEREST FORMULAS THIS IS 9 =50000*((1-(1+0.15)^6*(1+0.12)^-6)/(0.12-0.15)) 10 11 PW= $286,447.62 USING ELECTRONIC INTEREST TABLES THIS IS =$50,000*(P|A1 12%,15%,6) 12 13 14 SEE BELOW FOR TABULATED CASH FLOWS TO CONFIRM THE ANSWER. 15 16 EOY CF 17 0 18 1 $50,000.00 19 2 $57,500.00 20 3 $66,125.00 21 4 $76,043.75 22 5 $87,450.31 23 6 $100,567.86 24 25 PW= $286,447.62 USING EXCEL'S NPV FUNCTION THIS IS 26 =NPV(12%,CF YR 1:CF YR 6)+0

1 2 3 4 5 6 7 8 9 10 11 12 13 HE ANSWER. 14 15 16 17 18 19 20 21 22 23 24 25 26

A B C D E F 1 PROBLEM 2.133 2 3 i= 7.00% COMPOUNDED ANNUALLY 4 j= -40.00% COMPOUNDED ANNUALLY 5 n= 4 A1= 6 $60,000.00 7 8 PW= $115,038.00 USING INTEREST TABLES THIS IS =$60,000*(P|A1 7%,-40%,4) 9 10 11 PW= $115,037.72 USING FORMULAS THIS IS 12 =60000*((1-(1-0.4)^4*(1+0.07)^-4)/(0.07-(-0.4))) 13 14 SEE BELOW FOR TABULATED CASH FLOWS TO CONFIRM THE ANSWER. 15 16 EOY CF 17 0 $0.00 18 1 $60,000.00 19 2 $36,000.00 20 3 $21,600.00 21 4 $12,960.00 22 23 PW= $115,037.72 USING EXCEL'S NPV FUNCTION THIS IS 24 =NPV(7%,60000,36000,21600,12960)+0

A B C D 1 PROBLEM 2.134 2 3 i= 15.00% 4 j= 6.00% 5 n= 20 A1= 6 $1,000.00 7 8 PW= $8,933.81 TABLES FROM APPENDIX A =$1,000*(P|A1 15%,6%,20) 9 10 11 PW= $8,933.81 TABLES FROM PROBLEM 2.123 =$1,000*(P|A1 15%,6%,20) 12 13 14 USING TABULATED CASH FLOWS 15 16 EOY CF 17 0 $0.00 18 1 $1,000.00 19 2 $1,060.00 20 3 $1,123.60 21 4 $1,191.02 22 5 $1,262.48 23 6 $1,338.23 24 7 $1,418.52 25 8 $1,503.63 26 9 $1,593.85 27 10 $1,689.48 28 11 $1,790.85 29 12 $1,898.30 30 13 $2,012.20 31 14 $2,132.93 32 15 $2,260.90 33 16 $2,396.56 34 17 $2,540.35 35 18 $2,692.77 36 19 $2,854.34 37 20 $3,025.60 38 39 PW= $8,933.81 USING EXCEL'S NPV FUNCTION THIS IS 40 =NPV(15%,CF YR 1:CF YR 20)+0

A 1 PROBLEM 2.135 2 3 4 5 6 7 8 9 10 11 12

i= j= n= A1=

5.00% 10.00% 5 $1,000.00

PW= $5,237.53 USING INTEREST TABLES THIS IS =$1,000*(P|A1 5%,10%,5) PW= $5,237.53 USING EXCEL'S NPV FUNCTION THIS IS =NPV(5%,1000,1000*1.1,1000*1.1^2,1000*1.1^3,1000*1.1^4)

I 1 2 3 4 5 6 7 8 9 10 11 12

A 1 PROBLEM 2.136 2 3 4 5 6 7 8 9 10 11

i= j= n= A1=

5.00% 15.00% 7 $4,000.00

F= $50,116.76 USING INTEREST TABLES THIS IS =$4,000*(F|A1 5%,15%,7) F= $50,116.78 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS =FV(5%,7,,NPV(5%,4000,4000*1.15,4000*1.15^2,4000*1.15^3,4000* 1.15^4,4000*1.15^5,4000*1.15^6))

A 1 PROBLEM 2.137 2 3 4 5 6 7 8 9 10 11 12

i= j= n= A1=

10.00% 5.00% 6 $9,000.00

PW=

$43,839.18 USING INTEREST TABLES THIS IS =$9,000*(P|A1 10%,5%,6)

PW=

$43,839.17 USING EXCEL'S NPV FUNCTION THIS IS =NPV(10%,9000,9000*1.05,9000*1.05^2,9000*1.05^3,9 000*1.05^4,9000*1.05^5)

A B C D E F G H 1 PROBLEM 2.138 2 3 i= 10.00% 4 j= 15.00% 5 n= 4 A1= $2,000.00 6 7 8 a PW= $7,783.80 USING INTEREST TABLES THIS IS =$2,000*(P|A1 10%,15%,4) 9 10 11 PW= $7,783.79 USING EXCEL'S NPV FUNCTION THIS IS 12 =NPV(10%,2000,2000*1.15,2000*1.15^2,2000*1.15^3) 13 14 b A= $2,455.56 USING INTEREST TABLES THIS IS 15 =$7,783.80*(A|P 10%,4) 16 17 A= $2,455.56 USING EXCEL'S PMT FUNCTION THIS IS 18 =PMT(10%,4,-7783.79)

A B C D E F G H 1 PROBLEM 2.139 2 3 i= 15.00% 4 j= 10.00% 5 n= 5 A1= $14,000.00 6 7 8 a PW= $55,801.76 USING INTEREST TABLES THIS IS =$14,000*(P|A1 15%,10%,5) 9 10 11 PW= $55,801.73 USING EXCEL'S NPV FUNCTION THIS IS =NPV(15%,14000,14000*1.1,14000*1.1^2,14000*1.1^3,14 12 000*1.1^4) 13 14 b A= $16,646.78 USING INTEREST TABLES THIS IS 15 =$55,801.76*(A|P 15%,5) 16 17 A= $16,646.52 USING EXCEL'S PMT FUNCTION THIS IS 18 =PMT(15%,5,-55801.73)

A 1 PROBLEM 2.140 2

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

NOTE THAT THE WORDING OF THIS PROBLEM IMPLIES THE 18 DEPOSITS START AT BIRTH (BEGINNING OF YEAR 1) AND CONTINUE THROUGH BEGINNING OF YEAR 18. THEN, THE AMOUNT AT THE END OF YEAR 18 IS REQUESTED. i= j= n= A1=

6.00% 15.00% 18 $1,500.00 AT BEGINNING OF YEAR 1

FW= $168,206.35 USING INTEREST TABLES THIS IS =$1,500*(F|A1 6%,15%,18)*(F|P 6%,1) FW= $168,206.35 USING INTEREST TABLES FROM PROBLEM 2.123 =$1,500*(F|A1 6%,15%,18)*(F|P 6%,1) USING TABULATED CASH FLOWS EOY CF 0 $1,500.00 1 $1,725.00 2 $1,983.75 3 $2,281.31 4 $2,623.51 5 $3,017.04 6 $3,469.59 7 $3,990.03 8 $4,588.53 9 $5,276.81 10 $6,068.34 11 $6,978.59 12 $8,025.38 13 $9,229.18 14 $10,613.56 15 $12,205.59 16 $14,036.43 17 $16,141.90 18 $0.00 FW= $168,206.36 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS =FV(6%,18+1,,-NPV(6%,CF YR 0:CF YR 18))

A B C D E F G H 1 PROBLEM 2.141 2 3 i= 15.00% 4 j= 10.00% 5 n= 5 A1= $140,000.00 6 7 8 PW= $558,017.60 USING INTEREST TABLES THIS IS =$140,000*(P|A1 15%,10%,5) 9 10 11 PW= $558,017.60 USING INTEREST TABLES FROM PROBLEM 2.123 =$140,000*(P|A1 15%,10%,5) 12 13 14 USING TABULATED CASH FLOWS 15 16 EOY CF 17 0 $0.00 18 1 $140,000.00 19 2 $154,000.00 20 3 $169,400.00 21 4 $186,340.00 22 5 $204,974.00 23 24 PW= $558,017.31 USING EXCEL'S NPV FUNCTION THIS IS 25 =NPV(15%,CF YR 1:CF YR 5)+0

1 2

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

A PROBLEM 2.142

IN THIS PROBLEM, IT IS MUCH EASIER TO USE A SPREADSHEET AND TO KEEP LABOR, MATERIAL, AND OVERHEAD SEPARATE UNTIL COMBINED. i=

11.00% LABOR -5.00% $2,000,000.00

MATERIAL 4.00% $3,000,000.00

OVERHEAD 8.00% $1,600,000.00

TOTAL

j= A1= EOY 0 1 2 3 4 5 6 7

$0.00 $2,000,000.00 $1,900,000.00 $1,805,000.00 $1,714,750.00 $1,629,012.50 $1,547,561.88 $1,470,183.78

$0.00 $3,000,000.00 $3,120,000.00 $3,244,800.00 $3,374,592.00 $3,509,575.68 $3,649,958.71 $3,795,957.06

$0.00 $1,600,000.00 $1,728,000.00 $1,866,240.00 $2,015,539.20 $2,176,782.34 $2,350,924.92 $2,538,998.92

$0.00 $6,600,000.00 $6,748,000.00 $6,916,040.00 $7,104,881.20 $7,315,370.52 $7,548,445.51 $7,805,139.75

$8,295,499.60 $15,693,016.73 $9,307,846.73 $33,296,363.05 USING EXCEL'S NPV FUNCTION, EACH COLUMN IS =NPV(11%,CF YR 1:CF YR 7)+0

$8,295,500.00 $15,693,030.00 $9,307,840.00 $33,296,370.00 USING INTEREST TABLES FROM PROBLEM 2.123 =$2,000,000.00*(P|A1 11%,-5%,7) =$3,000,000.00*(P|A1 11%,4%,7)

27 28 29 30 31 32 33 34 35 36

=$1,600,000.00*(P|A1 11%,8%,7) c

$7,065,996.66 USING EXCEL'S PMT FUNCTION THIS IS =PMT(11%,7,-33296363.05)

$7,066,155.64 USING INTEREST TABLES THIS IS =$33,296,370.00*(A|P 11%,7) NOTE! TABLES DO NOT SUPPORT THIS LEVEL OF PRECISION

A B C D E F G H 1 PROBLEM 2.143 2 3 i= 8.00% 4 j= 5.00% 5 n= 10 6 SALARY $70,000.00 7 % DEPOSITED 10.00% A1= 8 $7,000.00 9 10 FW= $123,673.76 USING INTEREST TABLES THIS IS =$7,000*(F|A1 8%,5%,10) 11 12 13 FW= $123,673.76 TABLES FROM PROBLEM 2.123 =$7,000*(F|A1 8%,5%,10) 14 15 16 USING TABULATED CASH FLOWS 17 18 EOY CF 19 0 $0.00 20 1 $7,000.00 21 2 $7,350.00 22 3 $7,717.50 23 4 $8,103.38 24 5 $8,508.54 25 6 $8,933.97 26 7 $9,380.67 27 8 $9,849.70 28 9 $10,342.19 29 10 $10,859.30 30 31 FW= $123,673.75 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS 32 =FV(8%,10,,-NPV(8%,CF YR 1:CF YR 10)+0)

A B C D E F 1 PROBLEM 2.144 2 3 i= 15.00% 4 j= 10.00% 5 n= 5 6 P= $50,000.00 7 8 P= $50,000.00 USING INTEREST TABLES THIS IS =A1*(P|A1 15%,10%,5) 9 10 A1= 11 $12,544.41 =50000/3.98584 12 13 a SMALLEST PAYMENT $0.00 14 15 b LARGEST PAYMENT $18,366.27 =12544.41*(1+0.1)^4 16 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. 17 WILL USE SOLVER TO FIND VALUE OF A1. 18 BEGIN BY DEDICATING A CELL FOR A1 AND LET IT TAKE ON ANY VALUE AS IF IT WERE CORRECT. IT WILL BE CHANGED TO THE CORRECT 19 VALUE WHEN SOLVER IS USED. 20 A1= 21 $12,544.41 SOLVER CHANGED CELL 22 23 EOY CF 24 0 25 a 1 $12,544.41 26 2 $13,798.86 27 3 $15,178.74 28 4 $16,696.61 29 b 5 $18,366.28 30 31 P= $50,000.00 SOLVER TARGET CELL 32 USING EXCEL'S NPV FUNCTION THIS IS 33 =NPV(15%,CF YR 1:CF YR 5)+0

A 1 PROBLEM 2.145 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

i= 6.00% j= 4.00% n= 5 A1= $15,000.00 FW= $91,179.45 TABLES FROM APPENDIX A =$15,000*(F|A1 6%,4%,5) USING TABULATED CASH FLOWS EOY CF 0 $0.00 1 $15,000.00 2 $15,600.00 3 $16,224.00 4 $16,872.96 5 $17,547.88 FW= $91,179.51 USING EXCEL'S FV AND NPV FUNCTIONS THIS IS =FV(6%,5,,-NPV(6%,CF YR 1:CF YR 5)+0)

A 1 PROBLEM 2.146 2 3 4 5 6 7 8 9 10

11 12 13 14 15 16 17 18 19 20 21 22 23 24

25 26

TO GO FROM NOMINAL ANNUAL TO EFFECTIVE ANNUAL NOMINAL ANNUAL INTEREST RATE (E.G., 10.000%) COMPOUNDING PERIODS PER YEAR (E.G., 4 FOR QUARTERLY)

r= m=

10.000% USED r=10% FOR EXAMPLE 4 USED m=4 FOR EXAMPLE

EFFECTIVE ANNUAL INTEREST RATE

ieff= 10.381%

EFFECTIVE ANNUAL INTEREST RATE

USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.1/4)^4-1 ieff= 10.381% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(10%,4)

TO GO FROM EFFECTIVE ANNUAL TO NOMINAL ANNUAL EFFECTIVE ANNUAL INTEREST RATE (E.G., 10.381%) COMPOUNDING PERIODS PER YEAR (E.G., 4 FOR QUARTERLY)

ieff= 10.381%

NOMINAL ANNUAL INTEREST RATE

4 USED m=4 FOR EXAMPLE

10.000% USED r=10% FOR EXAMPLE USING COMPOUND INTEREST FORMULAS THIS IS =4*((1+0.10381)^(1/4)-1)

A 1 PROBLEM 2.147 2 3 4 5 6 7 8 9 10 11 12 13 14

i= 0.75% PER MONTH n= 480 MONTHS F= $2,000,000.00 A=

$427.23 USING COMPOUND INTEREST FORMULAS THIS IS =2000000*(0.0075/((1+0.0075)^480-1))

$427.22 USING INTEREST TABLES THIS IS =$2,000,000*(A|F 0.75%,480)

$427.23 USING EXCEL'S PMT FUNCTION THIS IS =PMT(0.75%,480,,-2000000)

A B C D E 1 PROBLEM 2.148 2 3 P= $12,000.00 4 i= 0.75% PER MONTH 5 A= $400.00 PER MONTH 6 7 n= 34.1129207 MONTHS USE 35 MONTHS 8 USING EXCEL'S NPER FUNCTION THIS IS 9 =NPER(0.75%,-400,12000) 10 11 CAN ALSO USE SOLVER TO FIND n 12 13 n= 34.1129208 <--SOLVER CHANGED CELL USE 35 MONTHS 14 15 A= $400.00 <--SOLVER TARGET CELL 16 USING EXCEL'S PMT FUNCTION THIS IS 17 =PMT(0.75%,n,-12000) 18 19 SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER. 20 21 EOY CF PW 22 23 0 24 1 $400.00 $397.02 25 2 $400.00 $791.09 26 3 $400.00 $1,182.22 27 4 $400.00 $1,570.44 28 5 $400.00 $1,955.78 29 6 $400.00 $2,338.24 30 7 $400.00 $2,717.86 31 8 $400.00 $3,094.65 32 9 $400.00 $3,468.63 33 10 $400.00 $3,839.83 34 11 $400.00 $4,208.27 35 12 $400.00 $4,573.97 36 13 $400.00 $4,936.94 37 14 $400.00 $5,297.21 38 15 $400.00 $5,654.80 39 16 $400.00 $6,009.73 40 17 $400.00 $6,362.01 41 18 $400.00 $6,711.67 42 19 $400.00 $7,058.73 43 20 $400.00 $7,403.21 44 21 $400.00 $7,745.12 45 22 $400.00 $8,084.49 46 23 $400.00 $8,421.33 47 24 $400.00 $8,755.66 48 25 $400.00 $9,087.50 49 26 $400.00 $9,416.88 50 27 $400.00 $9,743.80 51 28 $400.00 $10,068.28 52 29 $400.00 $10,390.36 53 30 $400.00 $10,710.03 54 31 $400.00 $11,027.33 55 32 $400.00 $11,342.26 56 33 $400.00 $11,654.85 57 34 $400.00 $11,965.11

A 58 59 60 61 62 63

B 35 36 37 38 39 40

C $400.00 $400.00 $400.00 $400.00 $400.00 $400.00

D $12,273.06 $12,578.72 $12,882.11 $13,183.23 $13,482.12 $13,778.78

E FIRST PW OF >= $12,000

A 1 PROBLEM 2.149 2 3 a 4 5 6 7 8 9 10 11 b 12 13 14 15 16 17 18 19 c 20 21 22 23 24 25 26 27 d 28 29 30 31 32 33 34 35 e 36 37 38 39 40 41

r= m=

10.00% 2

ieff= 10.2500% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.1/2)^2-1 ieff= 10.2500% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(10%,2) r= m=

10.00% 3

ieff= 10.3370% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.1/3)^3-1 ieff= 10.3370% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(10%,3) r= m=

10.00% 4

ieff= 10.3813% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.1/4)^4-1 ieff= 10.3813% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(10%,4) r= m=

10.00% 6

ieff= 10.4260% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.1/6)^6-1 ieff= 10.4260% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(10%,6) r= m=

10.00% 12

ieff= 10.4713% USING COMPOUND INTEREST FORMULAS THIS IS 10.4713% ieff= 10.4713% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(10%,12)

A 1 PROBLEM 2.150 2 3 a 4 5 6 7 8 9 10 11 b 12 13 14 15 16 17 18 19 c 20 21 22 23 24 25 26 27 d 28 29 30 31 32 33 34 35 e 36 37 38 39 40 41

r= m=

5.00% 2

ieff= ieff=

r= m= ieff= ieff=

5.0625% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.05/2)^2-1 5.0625% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(5%,2) 5.00% 3 5.0838% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.05/3)^3-1 5.0838% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(5%,3) 5.00% 4 5.0945% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.05/4)^4-1 5.0945% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(5%,4) 5.00% 6 5.1053% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.05/6)^6-1 5.1053% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(5%,6) 5.00% 12 5.1162% USING COMPOUND INTEREST FORMULAS THIS IS =(1+0.05/12)^12-1 5.1162% USING EXCEL'S EFFECT FUNCTION THIS IS =EFFECT(5%,12)

A 1 PROBLEM 2.151 2 3 4 5 6 7 8 9 10 11 12 13

r= 6.00% PER YEAR m= 12 i= 0.50% PER MONTH n= 60 MONTHS P= $50,000.00 A=

$966.50 USING INTEREST TABLES THIS IS =$50,000*(A|P 0.50%,60)

$966.64 USING EXCEL'S PMT FUNCTION THIS IS =PMT(0.5%,60,-50000)

A 1 PROBLEM 2.152 2 3 a 4 5 6 7 8 9 10 11 12 13 14 b 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

i= n= P=

0.50% PER MONTH 30 MONTHLY PAYMENTS $500.00

$17.99 USING INTEREST TABLES THIS IS =$500*(A|P 0.50%,30)

$17.99 USING EXCEL'S PMT FUNCTION THIS IS =PMT(0.50%,30,-500)

i= n= P= DELAY=

0.50% PER MONTH 30 MONTHLY PAYMENTS $500.00 12 MONTHS

FIRST, DETERMINE THE FUTURE WORTH OF THE ORIGINAL $500 AFTER 12 MONTHS. THEN, DETERMINE THE MONTHLY PAYMENT AMT12MO= $530.84 USING INTEREST TABLES THIS IS =$500.00*(F|P 0.5%,12) A=

$19.10 USING INTEREST TABLES THIS IS =$530.84*(A|P 0.50%,30)

AMT12MO= $530.84 USING EXCEL'S FV FUNCTION THIS IS =FV(0.5%,12,,-C16) A=

$19.10 USING EXCEL'S PMT FUNCTION THIS IS =PMT(0.5%,30,-530.84)

A B C D E F G H 1 PROBLEM 2.153 2 3 r= 6.000% 4 m= 2 5 YRS= 10 6 P= $4,000.00 7 8 FW= $7,224.44 USING COMPOUND INTEREST FORMULAS THIS IS 9 =4000*(1+0.06/2)^(2*10) 10 11 FW= $7,224.44 USING EXCEL'S FV FUNCTION THIS IS 12 =FV(0.06/2,2*10,,-4000) 13 14 OR, CAN USE THE EFFECTIVE RATE AS FOLLOWS 15 ieff= 16 6.090% USING EXCEL'S EFFECT FUNCTION THIS IS 17 =EFFECT(6%,2) 18 19 FW= $7,224.44 USING COMPOUND INTEREST FORMULAS THIS IS 20 =4000*(1+0.0609)^10 21 22 FW= $7,224.44 USING EXCEL'S FV FUNCTION THIS IS 23 =FV(6.09%,10,,-4000)

A B C D E F G H I 1 PROBLEM 2.154 2 3 r= 5.000% 4 m= 4 5 YRS= 4 6 F= $10,000.00 7 8 9 P= $8,197.50 USING INTEREST TABLES THIS IS 10 =$10,000*(P|F 1.25%,16) 11 12 P= $8,197.46 USING EXCEL'S PV FUNCTION THIS IS 13 =PV(0.05/4,4*4,,-10000) 14 15 OR, CAN USE THE EFFECTIVE RATE AS FOLLOWS 16 ieff= 17 5.09453% USING COMPOUND INTEREST FORMULAS THIS IS 18 =(1+0.05/4)^4-1 19 20 P= $8,197.46 USING COMPOUND INTEREST FORMULAS THIS IS 21 =10000*(1+0.0509453)^-4 22 23 P= $8,197.46 USING EXCEL'S PV FUNCTION THIS IS 24 =PV(5.09453%,4,,-10000)

A B C D E F G H 1 PROBLEM 2.155 2 3 a ANNUALLY 4 r= 7.000% 5 m= 1 6 YRS= 5 7 P= $10,000.00 8 9 F= $14,025.52 USING COMPOUND INTEREST FORMULAS THIS IS 10 =10000*(1+0.07/1)^(1*5) 11 F= $14,025.50 USING INTEREST TABLES THIS IS 12 =$10,000*(F|P 7%,5) 13 F= $14,025.52 USING EXCEL'S FV FUNCTION THIS IS 14 =FV(0.07/1,1*5,,-10000) 15 16 b QUARTERLY 17 r= 7.000% 18 m= 4 19 YRS= 5 20 P= $10,000.00 21 22 F= $14,147.78 USING COMPOUND INTEREST FORMULAS THIS IS 23 =10000*(1+0.07/4)^(4*5) 24 F= $14,147.80 USING INTEREST TABLES THIS IS 25 =$10,000*(F|P 1.75%,20) 26 F= $14,147.78 USING EXCEL'S FV FUNCTION THIS IS 27 =FV(0.07/4,4*5,,-10000) 28 29 c MONTHLY 30 r= 7.000% 31 m= 12 32 YRS= 5 33 P= $10,000.00 34 35 F= $14,176.25 USING COMPOUND INTEREST FORMULAS THIS IS 36 =10000*(1+0.07/12)^(12*5) 37 F= $14,176.25 USING ELECTRONIC INTEREST TABLES THIS IS 38 =$10,000*(F|P 7%/12,60) 39 F= $14,176.25 USING EXCEL'S FV FUNCTION THIS IS 40 =FV(0.07/12,12*5,,-10000) 41 42 d DAILY 43 r= 7.000% 44 m= 365 45 YRS= 5 46 P= $10,000.00 47 48 F= $14,190.20 USING COMPOUND INTEREST FORMULAS THIS IS 49 =10000*(1+0.07/365)^(365*5) 50 F= $14,190.20 USING ELECTRONIC INTEREST TABLES THIS IS 51 =$10,000*(F|P 7%/365,1825) 52 F= $14,190.20 USING EXCEL'S FV FUNCTION THIS IS 53 =FV(0.07/365,365*5,,-10000)

A B C D E F G H 1 PROBLEM 2.156 2 3 a ANNUALLY 4 r= 6.000% 5 m= 1 6 YRS= 8 7 F= $20,000.00 8 9 P= $12,548.25 USING COMPOUND INTEREST FORMULAS THIS IS 10 =20000*(1+0.06/1)^(-1*8) 11 P= $12,548.20 USING INTEREST TABLES THIS IS 12 =$20,000*(P|F 6%,8) 13 P= $12,548.25 USING EXCEL'S FV FUNCTION THIS IS 14 =PV(0.06/1,1*8,,-20000) 15 16 b SEMI-ANNUALLY 17 r= 6.000% 18 m= 2 19 YRS= 8 20 F= $20,000.00 21 22 P= $12,463.34 USING COMPOUND INTEREST FORMULAS THIS IS 23 =20000*(1+0.06/2)^(-2*8) 24 P= $12,463.40 USING INTEREST TABLES THIS IS 25 =$20,000*(P|F 3%,16) 26 P= $12,463.34 USING EXCEL'S FV FUNCTION THIS IS 27 =PV(0.06/2,2*8,,-20000) 28 29 c QUARTERLY 30 r= 6.000% 31 m= 4 32 YRS= 8 33 F= $20,000.00 34 35 P= $12,419.86 USING COMPOUND INTEREST FORMULAS THIS IS 36 =20000*(1+0.06/4)^(-4*8) 37 P= $12,419.80 USING INTEREST TABLES THIS IS 38 =$20,000*(P|F 1.5%,32) 39 P= $12,419.86 USING EXCEL'S FV FUNCTION THIS IS 40 =PV(0.06/4,4*8,,-20000) 41 42 d MONTHLY 43 r= 6.000% 44 m= 12 45 YRS= 8 46 F= $20,000.00 47 48 P= $12,390.48 USING COMPOUND INTEREST FORMULAS THIS IS 49 =20000*(1+0.06/12)^(-12*8) 50 P= $12,390.40 USING INTEREST TABLES THIS IS 51 =$20,000*(P|F 0.5%,96) 52 P= $12,390.48 USING EXCEL'S FV FUNCTION THIS IS 53 =PV(0.06/12,12*8,,-20000) 54 55 e WEEKLY 56 r= 6.000% 57 m= 52

A 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110

B YRS= F=

C 8 $20,000.00

$12,379.09 USING COMPOUND INTEREST FORMULAS THIS IS =20000*(1+0.06/52)^(-52*8) $12,379.00 USING INTEREST TABLES THIS IS =$20,000*(P|F 0.6/52%,416) $12,379.09 USING EXCEL'S FV FUNCTION THIS IS =PV(0.06/52,52*8,,-20000)

P= P=

DAILY r= m= YRS= F= P= P=

HOURLY r= m= YRS= F= P= P=

MINUTELY r= m= YRS= F= P= P=

SECONDLY r= m= YRS= F= P= P=

6.000% 365 8 $20,000.00 $12,376.16 USING COMPOUND INTEREST FORMULAS THIS IS =20000*(1+0.06/365)^(-365*8) $12,376.16 USING EXCEL'S FV FUNCTION THIS IS =PV(0.06/365,365*8,,-20000)

6.000% 8760 8 $20,000.00 $12,375.69 USING COMPOUND INTEREST FORMULAS THIS IS =20000*(1+0.06/8760)^(-8760*8) $12,375.69 USING EXCEL'S FV FUNCTION THIS IS =PV(0.06/8760,8760*8,,-20000)

6.000% 525600 8 $20,000.00 $12,375.67 USING COMPOUND INTEREST FORMULAS THIS IS =20000*(1+0.06/525600)^(-525600*8) $12,375.67 USING EXCEL'S FV FUNCTION THIS IS =PV(0.06/525600,525600*8,,-20000)

6.000% 31536000 8 $20,000.00 $12,375.67 USING COMPOUND INTEREST FORMULAS THIS IS =20000*(1+0.06/31536000)^(-31536000*8) $12,375.67 USING EXCEL'S FV FUNCTION THIS IS =PV(0.06/31536000,31536000*8,,-20000)

A 1 PROBLEM 2.157 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 a 29 30 31 32 33 b 34

BUILDING THE ACCOUNT r= 8.000% COMPOUNDED MONTHLY m= 12 MONTHS PER YEAR YRS= 20 A= $400.00 PER MONTH DETERMINE AMOUNT IN ACCOUNT AT END OF 20 YEARS, END OF MONTH 240 F(240)= $235,608.00 USING INTEREST TABLES THIS IS $400*(F|A 8/12%,240) F(240)= $235,608.17 USING EXCEL'S FV FUNCTION THIS IS =FV(0.08/12,12*20,-400) DETERMINE AMOUNT IN ACCOUNT AT END OF MONTH 251, ONE MONTH BEFORE 1ST WITHDRAWAL AT END OF MONTH 252 1ST WDL r= m= YRS=

252 MONTH 252 IS FIRST WITHDRAWAL 8.000% COMPOUNDED MONTHLY 12 MONTHS PER YEAR 15

F(251)=

$253,474.15 USING INTEREST TABLES THIS IS =$235608.00*(F|P 8/12%,11) $253,473.70 USING EXCEL'S FV FUNCTION THIS IS =FV(0.08/12,11,,-235608.17)

F(251)=

A= A=

$2,423.21 USING INTEREST TABLES THIS IS =$253,474.15*(A|P 8/12%,12*15) $2,422.33 USING EXCEL'S PMT FUNCTION THIS IS =PMT(0.08/12,12*15,-253473.7) $1,689.82 CALCULATING MONTHLY INTEREST ONLY =(0.08/12)*253473.7