Mathematics for Business and Economics
Exam Materials
Course Introduction
Mathematics for Business and Economics provides students with foundational mathematical tools essential for analyzing and solving real-world problems in business, finance, and economics. The course covers a range of topics including functions and graphs, systems of linear equations, matrix algebra, linear programming, and basic concepts of calculus such as differentiation and integration with emphasis on their applications in optimization, cost analysis, revenue and profit maximization, and economic modeling. Through practical examples and case studies, students learn how to interpret data, make informed decisions, and effectively apply quantitative methods to managerial and economic scenarios.
Recommended Textbook
Contemporary Business Mathematics with Canadian Applications 9th Edition by S. A. Hummelbrunner
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1484 Verified Questions
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Chapter 1: Review of Arithmetic
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Sample Questions
Q1) Florence Lamb is paid a commission of 10 3/4% on her net sales and is authorized to draw up to $900.00 a month. What is the amount due to Florence at the end of a month in which she drew $820.00, had sales of $14 660.00, and sales returns of $331.20?
Answer: Gross sales = $14660.00
Less: returns = 331.20
Net sales = 14328.80
Gross commission = 14328.80 × .1075 = 1540.35
Less: drawings 820.00
Amount due $720.35
Q2) Evaluate: 400(1 + .10 100/365)
Answer: 400 * (1 + .10 .2739726) =400 (1 + .02739726) = 400 (1.02739726) =410.959
Q3) A salesperson had gross earnings of $943.25 for last week on gross sales of $8 320.00. If returns and allowances were 5.5% of gross sales, what is his rate of commission based on net sales?
Answer: Net sales = (1 - .055) * 8320 = 7862.40 Commission rate = 11ea8930_3277_354f_b375_f989a0349565_TB4213_11 = 11.997%
Q4) Simplify: 5(4 + 3)
Answer: 5 7 = 35
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3
Chapter 2: Review of Basic Algebra
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Sample Questions
Q1) Simplify: 4(9y - 4) - 2(y - 1) - (1 - 3y)
Answer: 36y - 16 - 2y + 2 - 1 + 3y = 37y -15
Q2) Evaluate: (-0.1)<sup>7</sup>
Answer: -0.0000001
Q3) After reducing the regular selling price by 1/8, Sepaba Inc. sold a Stereo set for $300. What was the regular selling price?
Answer: Let the regular selling price be $x.
Reduction in price + $ 11ea8930_32ab_b211_b375_9350d6faf61b_TB4213_11 x x - 11ea8930_32ab_d922_b375_4b0c36c80e58_TB4213_11 x = 300 11ea8930_32ab_d923_b375_6f5543f50b62_TB4213_11 x = 300 x = $342.86
Q4) Simplify: (1 - r)2(1 - r)3(1 - r)
Answer: (1 - r)6
Q5) Simplify: 4x - 6y - 4x - 2y
Answer: -8y
Q6) Evaluate: (3)<sup>2</sup>(3)<sup>4</sup>
Answer: (3)<sup>2</sup>(3)<sup>4</sup> = 3<sup>6</sup> = 729
Q7) Express in exponential form: ln e5 = 5
Answer: e5 = e5
Page 4
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Chapter 3: Ratio, Proportion,
and Percent
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Sample Questions
Q1) A property owner listed his property for 172% more than he paid for it. The owner eventually accepted an offer 11 1/2% below his asking price and sold the property for $201 100. How much did the owner pay for the property?
Answer: 88 11ea8930_32cb_20f8_b375_fbb6542f3955_TB4213_11 % of asking price = sale price
.885 = 201100
A = $227,231.6384
List = C + 172% of C
$227,231.6384 = 1.72C
C = 132,111.42
Cost was $132,111.42.
Q2) 165% of what amount is $370?
Answer: 165% of x = 370
1.65x = 370 x = 224.24
Q3) Solve: 3.80:m = 10.8:8.10
Answer: 3.80:m = 10.8:8.10
10.8m = 3.80 8.10
m = 11ea8930_32b4_3dd6_b375_4773ce0464df_TB4213_11 m = 2.85
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Page 5
Chapter 4: Linear Systems
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Sample Questions
Q1) Solve graphically: 2y = x + 200 and 3x + 2y = 240
Q2) A machine requires 1 hours to make a unit of Product A, and 4 hours to make a unit of Product B. The machine operated for 195 hours producing a total of 80 units. How many hours were used to manufacture units of Product A?
Q3) Graph: y = 8
Q4) Solve the system of equations: 2x + 8y = -18
2x - 4y = 10
Q5) Find the slope of the line: 2y = 4(y + 2)
A) 0
B) 2
C) 4
D) 0.5
E) 1
Q6) Solve graphically: 4y = -5x and x = -6
Q7) The Oak Store has been producing 4640 chairs a day working two shifts. The second shift has produced 120 chairs fewer than four-thirds of the number of chairs produced by the first shift. Determine the number of chairs each shift has produced.
Q8) Solve the system of equations: 2.2x + 0.85y = 2.25 1.5x + 1.75y = 2.75
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Chapter 5: Trade Discount, Cash Discount, Markup, and Markdown
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Sample Questions
Q1) A dollar store bought 1000 pair of socks auctioned off en bloc for $2 000.00. This means that each pair of socks has the same cost. On inspection, the socks were classified as normal quality, seconds, and substandard. The 600 normal quality socks were sold at a markup of 90% of cost, the 300 pair of socks classified as seconds were sold at a markup of 30% of cost, and the socks classified as substandard were sold at 60% of their cost. What was the unit price at which each of the three classifications was sold?
A) $3.80, $2.60, $1.20
B) $3.80, $2.60, $3.20
C) $3.80, $3.20, $2.60
D) $3.80, $1.20, $2.60
E) $3.80, $1.20, $1.20
Q2) A wine merchant buys a case of wine for a listed price of $144.00 less 27% from a wine distributor. Overhead is 37% of cost and profit is 51% of cost. For how much should the item be retailed?
A) $159.78
B) $75.80
C) $211.35
D) $197.62
E) none of the above
Page 7
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Chapter 6: Break-Even and Cost-Volume-Profit Analysis
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Sample Questions
Q1) Last year a printing company had total sales of $37 500. The total of its variable costs was $15 000, and fixed costs were $18 000. Capacity is at sales maximum of $50 000.
a) Calculate the break-even point in (i) dollars of sales
(ii) as a percent of capacity
b) Draw a detailed break-even chart
Q2) A company has variable costs that are 4/7 the value of their sales revenues. Total net income for the most recent period was a profit of $53 770 and sales were $420 000. The company has started a new marketing campaign that they hope will increase sales, but it will require additional advertising of $6 400. How many sales dollars does the company have to generate in order to remain at the same level of profitability as before the new ad campaign?
A) $434 933.33
B) $326 357.50
C) $420 210.00
D) $140 396.67
E) $105 297.50
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Page 8
Chapter 7: Simple Interest
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Sample Questions
Q1) Debt payments of $1170.00 due two months ago and $1243.00 due today respectively are to be repaid by a payment of $1505.00 in one month and the balance in four months. If money is worth 8.4% p.a. and the agreed focal date is four months from now, what is the size of the final payment?
Q2) Debt payments of $800.00 due now and $1400.00 due in five months are to be repaid by a payment of $1000.00 in three months and a final payment in eight months. Calculate the size of the final payment if interest is 6%.
Q3) Calculate the amount of interest if $700.00 is invested at 5.5% for two years and nine months.
A) $111.65
B) $105.88
C) $10 587.50
D) $1058.75
E) $158.65
Q4) How many months will it take $639 to grow to $795 at 8.45% p.a.?
Q5) A loan of $1000 taken out on January 1 requires equal payments on February 1, March 1, and April 1. If the focal date is April 1, what is the size of the equal payments at 6.0%?
Q6) Determine the date represented by 100 days after March 1, 2012.
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Chapter 8: Simple Interest Applications
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Sample Questions
Q1) Dirk Propp borrowed $14 300.00 for investment purposes on May 19 on a demand note providing for a variable rate of interest and payment of any accrued interest on December 31. He paid $1300.00 on June 28, $1450 on September 25, and $4200.00 on November 15. How much is the final payment on December 31 if the rate of interest was 11.5% on May 19, 8.21% effective August 1, and 6.35% effective November 1? Use the declining balance method.
Q2) Sean purchased a 182-day, $10 000 T-bill on its issue date for $9 754.25. What was the original yield of the T-bill?
Q3) The maturity value of a five-month promissory note issued May 31, 2013, is $2 134.00. What is the present value of the note on the date of issue if money is worth 6.3%?
Q4) On July 12, 2013 a 140-day note promissory note for $9 175 with interest at 5.75% was issued. Find the proceeds of the note on September 30, 2013 if money is worth 7%.
Q5) Find the present value of a non-interest-bearing seven-month promissory note for $1 800 dated August 27, 2012, on December 4, 2012, if money is then worth 8.375%.
Q6) A 4-month, 7.26% percent promissory note dated June 10, 2013 has a maturity value of $6 231.34. What is the face value of the note?
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Page 10
Chapter 9: Compound Interest - Future Value and Present Value
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Sample Questions
Q1) Find m for the investment of $1000.00 for 2 years at 1.8% compounded semi-annually.
A) 4
B) 2
C) 0.9%
D) 1
Q2) An investment of $21700 is accumulated at 5.24% compounded quarterly for three and one-half years. At that time the interest rate is changed to 6.12% compounded monthly. How much is the investment worth two years after the change in interest rate?
Q3) A twenty-year note for $10000.00 bearing interest at 12% compounded monthly is discounted at 8% compounded quarterly four years and six months before maturity. Find the proceeds of the note.
Q4) Compute the discounted value of $5125.00 due in three years, eight months if money is worth 8.24% compounded quarterly.
Q5) An investment of $4300.00 earns interest at 9.96% p.a. compounded monthly for four years. At that time the interest rate is changed to 9% compounded semi-annually. How much will the accumulated value be two and a half years after the change?
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Chapter 10: Compound Interest - Further Topics
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Sample Questions
Q1) Determine the effective rate of interest corresponding to 6% p.a. compounded monthly
Q2) In how many years will money double at 8% compounded yearly?
A) 0.09 years
B) 0.9 years
C) 9.01 years
D) 90.1 years
E) 2 years
Q3) A financial obligation requires the payment of $1500.00 in nine months, $700.00 in twenty-one months, and $1700.00 in 33 months. When can the obligation be discharged by a single payment of $3900.00 if interest is 8.44% compounded quarterly?
Q4) Calculate the nominal rate of interest p.a. compounded semi-annually if $5000.00 accumulates to $7002.64 in 78 months.
A) 0.8656%
B) 0.02625%
C) 2.625%
D) 0.0525%
E) 5.25%
Q5) In how many years will money double at 6.62% compounded semi-annually?
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Chapter 11: Ordinary Simple Annuities
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Sample Questions
Q1) An annuity with periodic payments made at the end of each payment period is called:
A) ordinary
B) simple
C) annuity due
D) general
E) none of the above
Q2) In what period of time could you pay back a loan of $13900.00 by making monthly payments of $296.00 if interest is 6.5% compounded monthly?
Q3) Kam expects to retire in 22 years. Beginning one month after his retirement he would like to receive $590.00 per month for 25 years. How much must he deposit into a fund today to be able to do so if the rate of interest on the deposit is 6.12% compounded monthly?
Q4) Randy bought an annuity to pay him $2700.00 at the end of every six months for twenty years. How much of the total annuity payments is interest, if interest is 6.5% p.a. compounded semi-annually?
Q5) If a loan was repaid by quarterly payments of $715.00 over 7 years at 8.36% compounded quarterly, how much money had been borrowed?
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Chapter 12: Ordinary General Annuities
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Sample Questions
Q1) Calculate the accumulated value after ten years of payments of $1000.00 made at the end of each month if interest is 4% compounded semi-annually.
Q2) Mrs. Engleder has made deposits of $750.00 at the end of every six months for twenty-three years. If interest is 3.72% compounded monthly, how much will Mrs. Engleder have accumulated six years after the last deposit?
Q3) Mr. Sepaba accumulated $600 000.00 in an RRSP. He converted the RRSP into an RRIF and started to withdraw $3000.00 at the end of every month from the fund. If interest is 4.5% compounded yearly, for how long can Mr. Sepaba make withdrawals?
Q4) How much must be deposited at the end of each quarter for 5 years to accumulate to $27 000.00 at 6.84% compounded monthly?
Q5) Sabrina deposits $300.00 into a savings account at the end of each month for five years. If the accumulated value of the deposits is $20 000.00 and interest is compounded semi-annually, calculate the nominal rate of interest
Q6) A 21-year mortgage is amortized by making payments of $3052.61 at the end of every three months. If interest is 8.45% compounded annually, what was the original mortgage balance?
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Chapter 13: Annuities Due, Deferred Annuities, and Perpetuities
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Q1) Mrs. Martin contributes $1830.00 at the beginning of every three months to an RRSP. Interest on the account is 7.44% compounded quarterly.
a) What will the balance in the account be after 6 years?
b) How much of the balance will be interest?
c) If Mrs. Martin converts the balance after 6 years into an RRIF paying 5.41% compounded quarterly and makes equal quarterly withdrawals for 11 years starting three months after the conversion into the RRIF, what is the size of the quarterly withdrawal?
d) What is the combined interest earned by the RRSP and the RRIF?
Q2) How much does a depositor have to save at the beginning of every three months for 13.25 years to accumulate $41 600.00 if interest is 8% compounded quarterly?
Q3) TJ invested a retirement gratuity of $43 000.00 in an income averaging annuity paying 7% compounded monthly. He withdraws the money in equal monthly amounts over five years. If the first withdrawal is made nine months after the deposit, what is the size of each withdrawal?
Q4) A lease requires monthly payments of $1150.00 due in advance. If interest is 16% compounded quarterly and the term of the lease is 4 years, what is the cash value of the lease?
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Chapter 14: Amortization of Loans, Including Residential
Mortgages
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Q1) Andre has saved $152 000.00. If he withdraws $1750.00 at the beginning of every month and interest is 7.5% compounded monthly, what is the size of the last withdrawal?
Q2) The owner of the Pink Flamingo Motel borrowed $19 500.00 at 8.11% compounded semi-annually and agreed to repay the loan by making payments of $1110.00 at the end of every three months.
a) How many payments will be needed to repay the loan?
b) How much will be owed at the end of five years?
c) How much of the payments made at the end of five years will be interest?
Q3) Far East Imports Inc. owes $64 000.00 to be repaid by monthly payments of $2475.00. Interest is 6.12% compounded monthly.
a) How many payments will Far East Imports Inc. have to make?
b) How much interest is included in the 15th payment?
c) How much of the principal will be repaid by the 17th payment?
d) Construct a partial amortization schedule showing details of the first three payments, the last three payments, and totals.
Q4) A bank has an interest rate of 5% compounded semi annually for a five year closed mortgage. If the mortgage has monthly payments, calculate the effective rate of interest per each term.
Page 16
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Chapter 15: Bond Valuation and Sinking Funds
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Q1) A $50 000.00, 8% bond with quarterly coupons redeemable at par is purchased five years before maturity to yield 4% compounded semi-annually. Determine the premium or discount.
Q2) Three $25 000, 6% bonds with semi-annual coupons redeemable at par were bought eight years before maturity to yield 7% compounded semi-annually. Determine the gain or loss if the bonds are sold at 89.625 four years later.
Q3) A $50 000.00, 6% bond with semi-annual coupons redeemable at par in 14 years is purchased to yield 8% compounded semi-annually. What is the gain or loss if the bond is sold four years before maturity at 99.25?
Q4) A $1 000, 7% bond redeemable at par in eight years bears coupons payable annually. Compute the premium or discount and the purchase price if the yield, compounded annually, is:
a) 6.5%
b) 7.5%
c) 8.5%
Q5) A $100 000, 4% bond with semi-annual coupons is redeemable at 108. What is the purchase price to yield 5.5% compounded semi-annually seven years before maturity?
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Chapter 16: Investment Decision Applications
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Sample Questions
Q1) A company is looking to invest in a very risky project. They have a required rate of return of 27% compounded annually. The project has the following cash inflows: Year 1 $17500, Year 2 $15000, Year 3 $27500. It also has the following cash outflows: Immediately -$10000, Year 1 -$15000, Year 3 -$9500. What is the NPV?
A) $9718.06
B) $7918.06
C) $7819.06
D) $9918.06
E) -$9718.06
Q2) A project requires an initial outlay of $100 000 and promises net returns of $18500 per year over a twelve-year period. If the project has a residual value of $4000 after twelve years, what is the rate of return?
Q3) A contract is estimated to yield net returns of $7000.00 quarterly for seven years. To secure the contract, an immediate outlay of $80 000.00 and a further outlay of $60 000.00 three years from now are required. If interest is 6% compounded quarterly, determine if the investment should be accepted or rejected.
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