Mathematical Analysis for Business Exam Review
Course Introduction
Mathematical Analysis for Business explores the fundamental mathematical techniques and concepts essential for analyzing and solving business-related problems. The course covers topics such as functions, limits, differentiation, and integration, with a focus on practical applications to areas like optimization, cost-profit analysis, marginal analysis, and rate of change in business processes. Emphasis is placed on interpreting mathematical results in a real-world business context, enhancing students quantitative reasoning and decision-making skills necessary for the dynamic business environment.
Recommended Textbook
Contemporary Business Mathematics with Canadian Applications 9th Edition by S. A. Hummelbrunner
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Chapter 1: Review of Arithmetic
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Sample Questions
Q1) Last week April worked 44 hours. She is paid $11.20 per hour for a regular workweek of 40 hours and overtime at time and one-half regular pay.
a) What were April's gross wages for last week?
b) What is the amount of the overtime premium?
Answer: a) Regular earnings = 40 × 11.20 = 448.00
Overtime pay = 4 × 11.20 × 1.5 = 67.20
Gross earnings = $515.20
b) Overtime premium = 4 × 11.20 × 0.5 = $22.40
Q2) A salesperson is paid a weekly salary of $350.00 or a commission of 14.5% of his sales, whichever is the greater. What is his earnings for a week in which his sales were a) $2480.00?
b) $3780.00?
Answer: a) Salary = $350.00
Commission = .145 2480.00 = $359.60
Gross earnings = $709.60
b) Salary = $350.00
Commission = .145 3780.00 = $548.10
Gross earnings = $898.10
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Chapter 2: Review of Basic Algebra
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Sample Questions
Q1) Simplify: 57 ÷ 5-3
Answer: 57-(-3) = 510
Q2) Solve: 0.4x - 4 = 6 - 0.8x
Answer: .4x - 4 = 6 - .8x, 1.2x = 10, x = 8.33333333
Q3) Simplify: (-4)<sup>3</sup> ? (-4)
Answer: (-4)<sup>3+1 </sup>= (-4)<sup>4</sup> = 256
Q4) You have three colors of candies a jar - yellow, red and blue. There are 4 times plus 3 as many yellow candies as there are blue candies. There is 5/8 as many minus 6 red candies as there are blue. There are a total of 402 candies in the jar. How many of yellow, blue and red candies are there?
A) y-290, b-73, r-39
B) y-291, b-73, r-38
C) y-291, b-72, r-39
D) y-292, b-72, r-38
E) y-292, b-72, r-37
Answer: C
Q5) Evaluate: (-0.1)<sup>7</sup>
Answer: -0.0000001
Q6) Compute: ln 1.257
Answer: ln 1.257 = .228728
Page 4
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Chapter 3: Ratio, Proportion, and Percent
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Sample Questions
Q1) What amount is 8 1/3% less than $84?
Answer: x = 84 - 8 11ea8930_32c4_e036_b375_07b484ae2514_TB4213_11 % of 84 = 84 - 11ea8930_32c4_e037_b375_efbe5b1d8cfb_TB4213_11 84 = 84 - 7 = $77.00
Q2) Use Table 3.2 on page 128 of your textbook to convert C$900.00 to euros.
Answer: From the table, the exchange rate for Canadian dollars to euros is 0.7294. Conversion = 900 × 0.7294 =C$656.46
Q3) The number 500 is 62 1/2% more than what number?
Answer: 500 = x + 62.5% of x
x + 11ea8930_32c5_a38e_b375_09413b8327c9_TB4213_11 x = 500 = x + .625x 11ea8930_32c5_a38f_b375_45d0da957007_TB4213_11 x = 500 = 1.625x x = 307.69
Q4) A storekeeper bought merchandise for $1798. If she sells the merchandise at 33 1/3% above cost, how much gross profit does she make?
Answer: Let the gross profit be $x. x = 33 11ea8930_32c6_b509_b375_b3947b51844c_TB4213_11 % of 1798 = 11ea8930_32c6_dc1a_b375_1d1792899646_TB4213_11 1798 = $599.33
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Page 5
Chapter 4: Linear Systems
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Sample Questions
Q1) Graph: 3x + 4y = 12
Q2) Graph: y = 3 - 2x
Q3) Graph: y = 8
Q4) Find the slope of the line: 2y = 4(y + 2)
A) 0
B) 2
C) 4
D) 0.5
E) 1
Q5) Find the slope of the following: x + 5y = 10
A) 2
B) 0.5
C) 5
D) -0.2
E) 1
Q6) Find the slope and y-intercept: 3x + 2y = 10
Q7) A tavern holds 50 seats. Two types of seats are available the Friday night jazz festival: stage and dining. The cost of a stage seat is $15.00 and the cost of a dining seat is $5.00. If all 50 seats are sold the tavern would collect $400.00. How many of each type of seat is available?
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Chapter 5: Trade Discount, Cash Discount, Markup, and Markdown
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Sample Questions
Q1) A skateboard costing $16.23 was marked up to realize gross profit of 50% of the selling price.
a) What was the selling price?
b) What was the gross profit as a percent of cost?
Q2) What is the list price of an article that is subject to discounts of 40.5%, 10.4%, 5.0% if the net price is $650.00?
Q3) An invoice for $4755.00, dated March 27, terms 3/10 E.O.M., was received March 29. What payment must be made on April 10 to reduce the debt to $1900.00?
Q4) Christine Auto Sales and Service has an end of season sale on luxury cars. The original price was $67 998.00. The first discount is 10% and the second discount is 14%.
Calculate the final price of the cars.
A) $52 630.45
B) $51 678.48
C) $61 198.20
D) $58 478.28
E) $66 630.45
Q5) What is the selling price of an item bought for $1420.00 if the markup based on selling price is 59%?
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Sample Questions
Q1) A company that makes optical computer input devices has calculated their revenue and costs as follows for the most recent fiscal period: Sales $522 000
Costs:
Fixed Costs $145 000
Variable Costs 208 800
Total Costs 353 800
Net Income $168 200
What is the break-even point in sales dollars?
A) $362 500.00
B) $589 666.67
C) $241 666.67
D) $870 000.00
E) $280 333.33
Q2) Trevor, the new owner of the vehicle accessory shop is considering buying sets of winter tires for $299 per set and selling them at $520 each. Fixed costs related to this operation amount to $3 250 per month. It is expected that 18 sets per month could be sold. How much profit will Trevor make each month?
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8
Chapter 7: Simple Interest
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Sample Questions
Q1) On April 24, 2012, Rebecca purchased a government-guaranteed short-term investment maturing on July 5, 2012. How much did Rebecca pay for the investment if she will receive $6 000 on the maturity date and interest is 2.75%?
Q2) Debts of $1480.00 due four months ago and $1385.00 due in one month are to be settled by two equal payments due now and nine months from now respectively. Find the size of the equal payments at 12% p.a. with the agreed focal date now.
Q3) A loan payment of $1700 was due 60 days ago and another payment of $1200 is due 45 days from now. What single payment 90 days from now will pay off the two obligations if interest is to be 14% and the agreed focal date is 90 days from now?
Q4) Compute the accumulated value of $6 500.00 at 8.5% after eleven months.
Q5) What rate of interest did you receive over a period of 67 days if your principal was $7 444 and it has a maturity value of $7 601?
A) 11.94%
B) 11.49%
C) 11.69%
D) 11.29%
E) 11.99%
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Chapter 8: Simple Interest Applications
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Sample Questions
Q1) Compute the present value of a 150-day non-interest-bearing promissory note for $5 000 dated June 15, if the note was sold on August 21 and money is worth 6.5%.
Q2) Find the present value on June 1, 2014 of a non-interest-bearing note for $950 issued February 2, 2014, for 210 days if money is worth 8.31%.
Q3) Tracey bought a 182-day Government of Canada treasury bill at the price to yield an annual rate of return of 4.68%.
a) What was the price paid by Tracey if the T-bill has a face value of $100 000?
b) Later the same day, Tracey sold this T-bill to a large corporation to yield 4.48%. What was Tracey's profit on this transaction?
Q4) Find the maturity value of a six-month, $642 note dated November 1, 2013, earning interest at 7.5%.
Q5) 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%.
Q6) Find the maturity value of a 60-day, 4% note for $3000 note dated February 25, 2011.
Q7) Find the maturity value of a $473 note issued on October 4 at 8.5% for 190 days.
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Chapter 9: Compound Interest - Future Value and Present Value
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Sample Questions
Q1) The Get What You Pay For Bank advertises capital savings at 12% compounded monthly while Give Me Your Money Trust offers premium savings at 12.36% compounded yearly. Suppose you have $500.00 to invest for two years.
a) Which deposit will earn more interest?
b) What is the difference in the amount of interest?
Q2) How much will a registered retirement savings deposit of $10000.00 be worth in 15 years at 6.00% compounded quarterly? How much of the amount is interest?
Q3) Alternative Savings offers five-year term deposits at 10% compounded annually while your credit union offers such deposits at 9.6% compounded quarterly. If you have $1000 to invest, what is the maturity value of your deposit a) at Alternative Savings? b) at your credit union?
Q4) Determine the maturity value of $5400 due in 91 months compounding annually at 8.75%.
Q5) Use the exact method to determine the accumulated value of $3875.00 due in 61 months compounded annually at 9.75% p.a.
Q6) Determine the maturity value of $2000 due in 63 months compounding annually at 10%.
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Chapter 10: Compound Interest - Further Topics
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Sample Questions
Q1) 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
Q2) A financial obligation requires the payment of $250.00 in eighteen months, $350.00 in thirty months, and $300.00 in fifty-four months. When can the obligation be discharged by a single payment of $800.00 if interest is 5% compounded semi-annually?
Q3) If the effective rate of interest on an investment is 7%, what is the nominal rate of interest compounded quarterly?
Q4) Calculate the nominal annual rate of interest compounded quarterly that is equivalent to 10% p.a. compounded semi-annually.
Q5) Calculate the nominal rate of interest compounded semi-annually that is equivalent to 8.4% compounded monthly.
Q6) In how many years will money double at 6.62% compounded semi-annually?
Q7) In how many days will $770.00 grow to $880.00 at 11.5% p.a. compounded monthly?
Q8) In how many years will money triple at 12% compounded semi-annually?
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Chapter 11: Ordinary Simple Annuities
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Sample Questions
Q1) Compute the nominal annual rate of interest (compounded monthly) at which $200.00 deposited at the end of each month for ten years will amount to $30 000.00
Q2) Calculate the present value of 120 payments of $50.00 made at the end of each of 120 consecutive months respectively if money is worth 12% compounded monthly.
A) $3485.03
B) $3485.02
C) $6000.00
D) $3000.00
E) $34 850.30
Q3) What is the discounted value of deposits of $150.00 made at the end of each month for fourteen years if interest is 4.5% compounded monthly?
Q4) What is the nominal rate of interest if a six-year loan of $71000.00 is repaid by monthly payments of $1701.58?
Q5) The Savoias bought an investment property valued at $160000.00 by paying 25% down and mortgaging the balance over 25 years through equal monthly payments at 6% compounded monthly. What was the size of the monthly payments?
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Chapter 12: Ordinary General Annuities
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Sample Questions
Q1) A $360 000.00 mortgage is amortized by making monthly payments of $2600. If interest is 7.5% compounded semi-annually, what is the term of the mortgage?
Q2) A mortgage requires payments of $1000.00 at the end of every month for twenty-five years. If interest is 6% compounded semi-annually, calculate the principal of the loan.
A) $156,297.23
B) $155,206.86
C) $46,188.41
D) $300,000
E) $33,328.64
Q3) If a loan was repaid by semi-annual payments of $4720.00 in 6.5 years at 8.24% compounded quarterly, how much interest was paid?
Q4) 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?
Q5) Kelsey bought a car priced at $19700.00 for 10% down and equal monthly payments for 4.5 years. If interest is 8.22% compounded semi-annually, what is the size of the monthly payment?
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Chapter 13: Annuities Due, Deferred Annuities, and Perpetuities
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Sample Questions
Q1) Mrs. Lavergne deposits $562.71 at the beginning of every three months. Starting three months after the last deposit, she intends to withdraw $587.00 every three months for 16 years. If interest is 8.14% compounded quarterly, for how long must Mrs. Lavergne make deposits?
Q2) Quarterly deposits of $650.00 were made at the beginning of every 3 months for 11.25 years. If the interest is 4.92% compounded monthly, what amount can be withdrawn 6 years after the last deposit?
Q3) The amount of $75 400.00 is invested at 9.65% compounded quarterly for 3 years. After 3 years the balance in the fund is converted into an annuity. If interest on the annuity is 6.75% compounded semi-annually and payments are made at the end of every six months for 8 years, what is the size of the payments?
Q4) Monica would like to receive $3760.00 at the end of every six months for 8 years after her retirement. If she retires ten years from now and interest is 6.5% compounded semi-annually, how much must she deposit into an account every six months starting now?
Q5) Ellora wants to accumulate $150 000.00 in an RRSP by making annual contributions of $5000.00 at the beginning of each year. If interest is 5.5% compounded quarterly, calculate how long she has to make contributions.
Page 15
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Chapter 14: Amortization of Loans, Including Residential Mortgages
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Q1) The Taylors agreed to monthly payments rounded up to the nearest $100.00 on a mortgage of $136 000.00 amortized over 15 years. Interest for the first five years was 8.5% compounded semi-annually. After 30 months, as permitted by the mortgage agreement, the Taylors increased the rounded monthly payment by 10%.
a) Determine the mortgage balance at the end of the five-year term.
b) If the interest rate remains unchanged over the remaining term, how many more of the increased payments will amortize the mortgage balance?
c) How much did the Taylors save by exercising the increase-in-payment option?
Q2) A $248 000.00 mortgage amortized by monthly payments over 35 years is renewable after five years. Interest is 8.12% compounded semi-annually.
a) What is the size of the monthly payments?
b) How much interest is paid during the first year?
c) How much of the principal is repaid during the first five-year term?
d) If the mortgage is renewed for a further five-year term at 7.16% compounded semi-annually, what will be the size of the monthly payments?
Q3) A loan of $19 000.00 is repaid by quarterly payments of $900.00 each at 8% compounded quarterly. What is the principal repaid by the 21st payment?
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Chapter 15: Bond Valuation and Sinking Funds
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Sample Questions
Q1) A $150 000 bond bearing interest at 6% payable semi-annually is bought eight years before maturity to yield 4.5% compounded annually. If the bond is redeemable at par, what is the purchase price?
Q2) Annual sinking fund payments made at the beginning of every year for four years earning 4.5% compounded annually amount to $25 000.00 at the end of four years. Construct a sinking fund schedule showing totals.
Q3) A manufacturing company is planning a $600 000 expansion 6 years from now. By that time the company intends to accumulate 75% of the cost of the expansion by making payments into a sinking fund at the beginning of each of the next six years. Interest paid by the fund is 7% compounded annually. a) Calculate the size of annual payment into the fund. b) Calculate the total amount deposited into the fund. c) Calculate the amount of interest.
Q4) A $1000, 6% bond redeemable at par with semi-annual coupons was purchased 10 years before maturity to yield 5% compounded semi-annually. The bond was sold 3 years later at 102. Calculate the gain or loss on the sale of the bond.
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Chapter 16: Investment Decision Applications
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Q1) The owner of a video store is considering remodeling the store in order to carry a larger inventory. The cost of remodeling and additional inventory is $43 200. The expected increase in net profit is $7000 per year for the next 3 years and $10 000 each year for the following 7 years. After ten years, the owner plans to retire and sell the business. She expects to recover the additional $40 000 invested in inventory but not the $43 200 invested in remodeling. Compute the rate of return.
Q2) A once in a lifetime project requires an immediate outlay of $100 000 and $25 000 at the end of each year for 3 years. Net returns are nil for the first 3 years and $30 000 per year thereafter for fourteen years. What is the net present value of the project at 16%?
Q3) A new venture that requires outlays of $127 000 for each of the first two years will yield net returns of $85 000 in each year for years 3 to 6 and $70 000 for each of the following four years. A residual value of $130 000 can be recovered at the end of the last income period. Should the venture be undertaken if a yield of 11.56% is required?
Q4) Assume that the net present value of a project is $ 3870 at 10%, and -$1853 at 12%. Use linear interpolation to compute the rate of return correct to the nearest tenth of a percent.
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