Mathematics for Commerce
Textbook Exam Questions
Course Introduction
Mathematics for Commerce introduces students to the essential mathematical concepts and techniques used in business and financial contexts. This course covers topics such as percentages, simple and compound interest, annuities, profit and loss calculations, depreciation, break-even analysis, and introductory statistics. Emphasis is placed on problem-solving skills and the application of mathematical principles to real-life commercial scenarios, enabling students to make informed decisions in the fields of finance, accounting, and economics.
Recommended Textbook
Contemporary Business Mathematics with Canadian Applications 9th Edition by S. A. Hummelbrunner
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Page 2
Chapter 1: Review of Arithmetic
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Sample Questions
Q1) Emily's residence is assessed by the local taxation department at $249 500.00. Calculate the property taxes paid on this property if the existing mill rate is 15.
Answer: 249500 × 11ea8930_327b_540d_b375_7b0c02b417e3_TB4213_11 = $3742.50
Q2) Norm Bates is paid a semi-monthly salary of $792.50. Regular hours are 37 1/2 per week and overtime is paid at time and one-half regular pay.
a) What is Norm's hourly rate of pay?
b) How many hours overtime did Norm work in a pay period for which his gross pay was $946.30?
Answer: a) Annual salary = 792.50 × 24 = 19020.00
Weekly pay = 19020.00 ÷ 52 = 365.76923
Hourly rate of pay = 365.76923 ÷ 37.5 = $9.75
b) Gross earnings = 946.30
Regular earnings = 792.50
Overtime pay = 153.80
Overtime hourly rate = 9.75 × 1.5 = 14.625
Overtime hours = 153.80 ÷ 14.625 = 10.516 hr.
Q3) Simplify: 8 + 6 2
Answer: 8 + 12 = 20
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Chapter 2: Review of Basic Algebra
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Sample Questions
Q1) Compute: 1956<sup>2/5</sup>
Answer: 20.727529
Q2) Simplify: -3x(4 - 2b - b)
Answer: -12x + 6bx + 3bx = -12x + 9bx
Q3) Solve the following and check your solutions: 12x + 5(9 - x) = 429
A) 58.86
B) -58.86
C) 54.14
D) -54.14
E) -5.14
Answer: A
Q4) Evaluate: (1.05)<sup>0</sup>
Answer: 1
Q5) Simplify: (-4)<sup>4</sup> ? (-4)
Answer: (-4)<sup>4+1</sup> = (-4)<sup>5</sup> = -1024
Q6) Solve: 0.4x - 4 = 6 - 0.8x
Answer: .4x - 4 = 6 - .8x, 1.2x = 10, x = 8.33333333
Q7) Solve: x + 0.307x = 640.20
Answer: 1.307x = 640.20, x = 11ea8930_329c_492d_b375_8350d95422e5_TB4213_11 = 489.824
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Chapter 3: Ratio, Proportion, and Percent
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Sample Questions
Q1) If total deductions on a yearly salary of $28 600 amounted to 16 2/3%, how much was deducted?
Answer: Let the deduction be $x.
x = 16 11ea8930_32c1_f9ee_b375_870a5f679fce_TB4213_11 % of 28600 = 11ea8930_32c2_20ff_b375_81d19658876c_TB4213_11 × 28600 = $4766.67
Q2) Sales in June increased 16 2/3% over May sales. If June sales amounted to $27 535, what were May sales?
Answer: Let May sales be $x.
x + 16 11ea8930_32ca_abc4_b375_57c59729caf4_TB4213_11 % of x = 27535 x + 11ea8930_32ca_d2d5_b375_695e8a3d22d6_TB4213_11 x = 27535 11ea8930_32ca_d2d6_b375_29b9b304ec77_TB4213_11 x = 11ea8930_32ca_d2d7_b375_61c5664741b6_TB4213_11 x = 27535 x = 23601.43
May sales were $23601.43.
Q3) 166 2/3% of what amount is $280?
Answer: 166 11ea8930_32c3_809a_b375_2f7ccca5d872_TB4213_11 % of x = 280 11ea8930_32c3_809b_b375_593fd823c254_TB4213_11 x = 280 11ea8930_32c3_a7ac_b375_f1dcd4c87c1b_TB4213_11 x = 280 x = 280 11ea8930_32c3_a7ad_b375_5160a0957593_TB4213_11 x = $168
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Chapter 4: Linear Systems
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Sample Questions
Q1) Find the y-intercept for the following: 3x - 5y = 60
A) 12
B) -12
C) 60
D) -60
E) -5
Q2) Find the slope and y-intercept: 1.5x + 3y = 2.4
Q3) Graph: y = 8
Q4) Solve the system of equations: 0.8x + 0.3y = 1.3
0.3x + 0.2y = 1.1
Q5) 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?
Q6) Find the slope and y-intercept: 3y - 5 = 2(x - 2)
Q7) Solve graphically: 4x = -2y and x = 6
Q8) Solve the system of equations: 4x + 18y = 36
2x + 9y = -18
Q9) Solve the system of equations: 3x - 8y + 72 = 0
7x = 4y - 8
Q10) Find the slope and y-intercept: 4x + 5y = 31 Page 6
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Page 7
Chapter 5: Trade Discount, Cash Discount, Markup, and Markdown
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Sample Questions
Q1) A store has an end of season sale on snow blowers. The original price was $679.98. The first discount is 10% and the second discount is 14%. What is the final sale price of the snow blowers?
A) $526.30
B) $517.54
C) $541.01
D) $540.86
E) $529.40
Q2) The regular selling price of merchandise sold in a store includes a margin of 62% based on selling price. During a sale, an item which cost the store $231.25 was marked down 47%. For how much was the item sold?
Q3) An appliance store sells electric kettles at a markup of 23.6% of the selling price. The store's margin on a particular model is $7.78.
a) For how much does the store sell the kettles?
b) What was the cost of kettles to the store?
c) What is the percent markup based on cost?
Q4) What is the selling price of an item bought for $1420.00 if the markup based on selling price is 59%?
Q5) A 47% discount allowed on an article amounts to $3.57. What is the net price?
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Chapter 6: Break-Even and Cost-Volume-Profit Analysis
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Sample Questions
Q1) A local toolmaker makes the best hammers on the market. The head of the hammer costs $12.11 and the handle costs $4.37. It takes 1.4 minutes to assemble the hammer and the hourly cost is $90.00 for assembly time. The company has fixed operating costs of $22 310 per month. They sell the hammers for three times their total variable cost. The company wants to make a monthly profit of $5000. How many hammers must they sell?
A) 796
B) 735
C) 776
D) 766
E) 768
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?
Q3) Elaine's business budget included sales of $350 000 and fixed costs of $52 600. If the total contribution margin for the business was $125 000, what are the sales needed to break even?
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Chapter 7: Simple Interest
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Sample Questions
Q1) Compute the amount of interest for $500.00 at 8.75% from June 30 to December 31.
Q2) Determine the exact time between January 21, 2014 and September 13, 2014 by counting days.
Q3) Leo wishes to invest $8 000.00 that he saved from his summer job. His bank offers 3.75% for a one-year term investment or 3.5% for a six-month term. Help Leo to investigate his options.
a) How much will Leo receive after one year if he invests at the one-year rate?
b) How much will Leo receive after one-year if he invests for six-months at a time at 3.5% each time?
c) What would the one-year rate have to be to yield the same amount of interest as the investment described in part b)?
Q4) Compute the amount of interest on $250.00 at 8.25% p.a. from March 30, 2014 to October 28, 2014.
Q5) Determine the deposit that must be made to earn $49.27 in 325 days at 6%.
Q6) What is the present value of $41 230.00 due in nine months if interest is 11.1%?
Q7) 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%?
Page 10
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Chapter 8: Simple Interest Applications
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Sample Questions
Q1) Find the maturity value of a $1 190, 7.275%, 120-day note dated February 5, 2013.
Q2) 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.
Q3) Darren purchased $250 000 in 364-day T-bills 315 days before maturity to yield 2.86%. After holding it for 120 days, Darren sold the T-bill for a yield of 3.25%.
a) How much did Darren pay for the T-bills?
b) For how much did Darren sell the T-bills?
c) What rate of return (per annum) did Darren realize on the investment?
Q4) 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%.
Q5) Determine the maturity value of a 120-day note for $2 260.00 dated May 9 and bearing interest at 5.66%.
Q6) Find the maturity value of a $473 note issued on October 4 at 8.5% for 190 days.
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Page 11
Chapter 9: Compound Interest - Future Value and Present
Value
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Q1) 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?
Q2) Fahira invested $5000.00 at 4.8% compounded quarterly on January 1, 2012. On July 1, 2013 the rate changed to 5.6% p.a. compounded semi-annually. Calculate the amount Fahira will have on January 1, 2005.
Q3) Debts of $400.00, $450.00 and $500.00 are due in one year, eighteen months and thirty months from now respectively. Determine the single payment now that would settle the debts if interest is 8% p.a. compounded quarterly.
Q4) A loan of $8000.00 taken out two years ago is to be repaid by three equal installments due now, three years from now, and six years from now respectively. What is the size of the equal installments if interest on the debt is 7.32% p.a. compounded monthly?
Q5) Determine the sum of money that will grow to $18 530 in four years, eleven months at 5.2% compounded quarterly.
Q6) Suppose $4320.00 is invested for five years, eight months at 8.25% compounded annually. What is the compounded amount?
Page 12
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Chapter 10: Compound Interest - Further Topics
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Sample Questions
Q1) What nominal rate of interest-compounded quarterly will have to be earned on a savings account for it to grow from $1525 to $1955 over a period of 21 months?
A) 14.45%
B) 15.45%
C) 12.45%
D) 3.61%
E) 10.45%
Q2) Janice owes two debt payments, a payment of $6700 due in twelve months and a payment of $8750 due in twenty-one months. If Janice makes a payment of $7000 now, when should she make a second payment of $7900 if money is worth 11.5% compounded semi-annually?
Q3) A loan of $9000.00 was repaid together with interest of $3728.00. If interest was 9.4% compounded quarterly, how long was the loan taken out? (Give answer in years and months to the nearest tenth)
Q4) At what nominal rate of interest compounded monthly will $1700.00 earn $500.00 interest in three years?
Q5) In how many years will money triple at 12% compounded semi-annually?
Q6) In how many days will $770.00 grow to $880.00 at 11.5% p.a. compounded monthly?
Q7) 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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Q1) If a loan was repaid by ordinary monthly payments of $715.00 in seven years at 9.12%, compounded monthly, how much interest was paid?
Q2) 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
Q3) Planning for their child's college education, David and Carol Roberts opened an account paying 6.36% compounded monthly. If ordinary annuity payments of $700.00 per month are to be paid out of the account for three years starting seven years from now, how much did the Roberts' deposit?
Q4) How many monthly payments will it take for $1000.00 deposited at the end of each month to amount to $50000.00 at 9% compounded monthly?
Q5) The term of annuity is
A) the interval between the first and the last payments
B) the length of the payment interval
C) the length of time from the beginning of the first payment interval to the end of the last payment interval
D) the length of the conversion interval
E) the length of time between the successive payments
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Page 14
Chapter 12: Ordinary General Annuities
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Q1) What is the accumulated value of deposits of $2000.00 made at the end of every year for three years if interest is 6.00% compounded quarterly?
Q2) 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.
Q3) What is the discounted value of $3000.00 paid at the end of every six months for 5 years if interest is 8.00% compounded yearly?
Q4) You make 6 quarterly deposits starting at $135 and increasing at a constant rate of 4.5%. The interest rate is 8.4% compounded quarterly. What is the size of the last deposit?
A) $186.23
B) $168.23
C) $128.63
D) $135.00
E) $668.23
Q5) A real estate developer bought land for $170 000.00 down and monthly payments of $10450.00 for 5 years. What is the equivalent cash price if money is worth 7.75% compounded semi-annually?
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Page 15
Chapter 13: Annuities Due, Deferred Annuities, and Perpetuities
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Q1) Sheila intends to retire in 14 years and would like to receive $2472.00 every six months for 9 years starting on the date of her retirement. How much must Sheila deposit in an account today if interest is 6.65% compounded semi-annually?
Q2) A lease agreement valued at $15 000.00 requires payment of $900.00 at the beginning of every quarter for five years. What is the nominal rate of interest charged (compounded quarterly)?
Q3) What sum of money must be deposited in a trust fund to provide a scholarship of $630.00 payable at the end of each month if interest is 7.8% compounded monthly?
Q4) 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?
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Page 16
Chapter 14: Amortization of Loans, Including Residential
Mortgages
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Q1) John has agreed to purchase his partner's share in real estate by making payments of $5000.00 every three months. The agreed transfer value is $40000.00 and interest is 10% compounded annually. If the first payment is due at the date of the agreement, what is the size of the final payment?
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) Olfert Inc. is repaying a loan of $52 500.00 by making payments of $4700.00 at the end of every six months. If interest is 7.5% compounded semi-annually, construct an amortization schedule showing the total paid and the total cost of the loan.
Q4) 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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Page 17
Chapter 15: Bond Valuation and Sinking Funds
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Q1) Bonds in denominations of $100 000 redeemable at 104 are offered for sale. If the bonds mature in ten years and six months and the coupon rate is 5.5% payable quarterly, what is the market price of the bonds to yield 7.2% compounded quarterly?
Q2) A $25 000, 7% bond with semi-annual coupons redeemable at par in twenty-two years is purchased to yield 6% compounded semi-annually. Determine the gain or loss if the bond is sold seven years after the date of purchase at 98.25.
Q3) A $125 000 bond, redeemable at par in three years with 7.5% coupons payable quarterly, is bought to yield 6% compounded quarterly. (i) Compute the premium or discount and the purchase price. (ii) Construct a schedule for amortization of premium.
Q4) A $200 000, 6% bond with semi-annual coupons redeemable at par March 1, 2009, was purchased on November 15, 1999, to yield 5% compounded semi-annually. What was the purchase price of the bond?
Q5) A $5000.00 6.5% bond redeemable at 109 with interest payable annually is purchased six years before maturity to yield 7% compounded annually. Construct the appropriate bond schedule.
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Chapter 16: Investment Decision Applications
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Q1) A new car costs $21 000. Alternatively, the car can be leased for three years by making payments of $360 at the beginning of each month and can be bought at the end of the lease for $10 000. If interest is 8% compounded semi-annually, which alternative is preferable?
Q2) What is the IRR for the following net annual cash flows today -$45000, Year 1 +$12000, Year 2 +$37000, Year 3 +$12000, Year 4 +$17000?
A) 26.722%
B) 16.722%
C) 6.722%
D) 36.722%
E) 46.722%
Q3) A company is considering a project that will require a cost outlay of $30 000 per year for three years. At the end of the project, the company expects to salvage the physical assets for $50 000. The project is estimated to yield net returns of $60 000 in Year 4, $40 000 in Year 5, and $15 000 for each of the following five years. Alternative investments are available yielding a rate of return of 14.5%. Compute the net present value of the project.
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