Commercial Mathematics
Test Bank
Course Introduction
Commercial Mathematics is designed to equip students with practical mathematical skills used in business and financial environments. The course covers essential topics such as percentages, profit and loss, simple and compound interest, discounts, ratio and proportion, and basic statistics relevant to commerce. Students will learn how to apply mathematical methods to solve problems involving investments, sales transactions, taxation, and payroll calculations. Emphasis is placed on developing accuracy, logical reasoning, and analytical abilities, enabling learners to make informed decisions and efficiently tackle quantitative challenges in real-world commercial settings.
Recommended Textbook
Contemporary Business Mathematics with Canadian Applications 9th Edition by S. A. Hummelbrunner
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16 Chapters
1484 Verified Questions
1484 Flashcards
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Page 2
Chapter 1: Review of Arithmetic
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103 Flashcards
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Sample Questions
Q1) Change 0.25% into a decimal.
Answer: 0.25/100=0.0025
Q2) R.J. earns $11.70 an hour, with time-and-a-half for hours worked over 36 a week. His clock hours for a week are 10.5, 7.5, 11, 13, and 9.75. Determine his gross earnings for a week.
Answer: Total hours = 10.5 + 7.5 + 11 + 13 + 9.75 = 51.75
Regular weekly earnings = 36 × $11.70 = $421.20
Overtime earnings = (51.75 - 36) × $11.70 × 1.5 = $276.41
Gross = Regular time + Overtime = $421.20 + $276.41 = $697.61
Q3) Nick's gross earnings for one week was $698.10. His regular rate of pay is $15.60 for a 35 hour week and overtime is paid at time and one-half regular pay. Calculate the number of hours that Nick worked.
Answer: Gross earnings =698.10
Regular earnings = 35 × 15.60 = 546.00
Overtime pay = 698.10 - 546.00 = 152.10
Overtime hours = 11ea8930_327e_1337_b375_d34235267ace_TB4213_11 = 6.5 hours
Total number of hours worked = 35 + 6.5 = 41.5 hours
Q4) Simplify: (14 + 7)/3
Answer: (14 + 7)/3 = 21/3 = 7
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Chapter 2: Review of Basic Algebra
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193 Verified Questions
193 Flashcards
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Sample Questions
Q1) Simplify: (5x - 4)(3x +1)
A) 15x2 - 7x + 4
B) 15x2 - 7x - 4
C) 15x2 + 7x - 4
D) -15x2 - 7x + 4
E) -10x2 - 7x + 4
Answer: B
Q2) Evaluate: (-5)<sup>-3</sup>
Answer: - 11ea8930_328f_509d_b375_25ffa7f29bb0_TB4213_11 or -.008
Q3) Evaluate: ln 60
Answer: ln 60 = 4.094344562
Q4) Compute: ln[3.00e<sup>-.3</sup>]
Answer: ln(3.00e<sup> -.3</sup>) = ln 3.00 + ln e<sup>-.3</sup> = ln 3.00 - .3 ln e = 1.0986123 -.3 = .7986123
Q5) Simplify: (4a - 1)(a - 3a + 1)
Answer: 4a2 - 12a2 +4a - a + 3a - 1 = -8a2 + 6a - 1
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Chapter 3: Ratio, Proportion, and Percent
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152 Verified Questions
152 Flashcards
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Sample Questions
Q1) Suppose it costs $363.50 Canadian to purchase $350.00 U.S.
a) What is the exchange rate?
b) How many U.S. dollars will you receive if you convert $925 Canadian into U.S. dollars?
Answer: a) Exchange rate U.S$ per C$ =
11ea8930_32cf_3fca_b375_fd36bae0eac4_TB4213_11 = .962861
C$1 = US$0.962861.
b) C$925.00 = 925.00(0.962861) = US$890.65.
Q2) If one Canadian dollar is equivalent to $0.9421 U.S., how much do you need in Canadian funds to buy $1000 U.S.?
Answer: Let the number of Canadian dollars be x.
11ea8930_32cf_dc10_b375_773f062f5465_TB4213_11 =
11ea8930_32d0_0321_b375_db3f57935b61_TB4213_11
11ea8930_32d0_0322_b375_8780667c0b62_TB4213_11 = 11ea8930_32d0_2a33_b375_93b4166a13e0_TB4213_11 x = 11ea8930_32d0_2a34_b375_07c013c197f9_TB4213_11 = 1061.46
$1000.00 U.S. costs $1 061.46 Canadian.
Q3) Set up a ratio to represent the following: one-half of an hour to 18 minutes
Answer: 30:18 5:3
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Chapter 4: Linear Systems
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81 Flashcards
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Sample Questions
Q1) Find the slope and y-intercept: 4.5x + 9y = 81
Q2) Solve the system of equations: x + 7y = 0 x + 4y = 8
Q3) Solve graphically: 4y = -5x and x = -6
Q4) Solve the system graphically.
3x - 7 = y
6x -2 y = 14
Q5) Solve graphically: 2x = -5y and 3x + y = 9
Q6) A theatre holds 400 seats. Two types of seats are available: orchestra and balcony. The cost of an orchestra seat is $60.00 and the cost of a balcony seat is $45.00. If all 400 seats are sold the theatre would collect $22 500.00. How many of each type of seat is available?
Q7) A machine requires 3 hours to make a unit of Product A, and 6 hours to make a unit of Product B. The machine operated for 195 hours producing a total of 40 units. How many hours were used to manufacture units of Product A?
Q8) Find the slope and y-intercept: 2x - y = 8
Q9) Solve graphically: x - y = 4 and x + y = 6
Q10) Graph: y = 8
Q11) Graph: 3x + 4y = 12 Page 6
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Page 7
Chapter 5: Trade Discount, Cash Discount, Markup, and Markdown
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119 Verified Questions
119 Flashcards
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Sample Questions
Q1) 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?
Q2) A fierce price war has broken-out over gas. Super-Save offered pre-price war gas at 73.9 cents per litre with 5% Super-Save discount. Cooperative gas was 75.9 cents per litre and they offered a 3%, 10% discount. What additional discount must Super-Save offer to beat their competitor's price by 2%?
A) -79.325%
B) 89.513%
C) 31.889%
D) 7.506%
E) 8.105%
Q3) The net price of an article is $125.46. What is the list price if a discount of 38% was allowed?
A) $200.90
B) $204.13
C) $202.35
D) $90.91
E) $738.00
Q4) 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 company that makes environmental measuring devices has calculated their revenue and costs as follows for the most recent fiscal period: Sales $750 000 Costs:
Fixed Costs $200 000
Variable Costs 250 000
Total Costs 450 000
Net Income $300 000
What is the break-even point in sales dollars?
A) $100 000
B) $200 000
C) $300 000
D) $250 000
E) $450 000
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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Chapter 7: Simple Interest
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Sample Questions
Q1) Determine the exact time between January 21, 2014 and September 13, 2014 by counting days.
Q2) In how many months will $5 000 grow to $6 000.00 at 9.5% p.a.?
Q3) Compute the amount of interest on $875.00 at 11.5% p.a. from May 29, 2013 to August 13, 2013.
Q4) Compute the amount of interest for $500.00 at 8.75% from June 30 to December 31.
Q5) What is the amount to which $7 250.00 will grow at 7.75% p.a. in 3 months?
Q6) 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%
Q7) Determine the deposit that must be made to earn $49.27 in 325 days at 6%.
Q8) An investment of $12 000.00 earns an interest of $480.00. Calculate the time in months if the interest rate is 6%.
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Q9) Find the maturity value of $832.00 invested at 8.8% from May 20, 2013, to November 23, 2013.
Chapter 8: Simple Interest Applications
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Sample Questions
Q1) 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?
Q2) 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?
Q3) A government of Ontario 364-day T-bills with a face value of $50 000 were purchased on January 2 for $48 000.76. The T-bills were sold on September 28 for $48 999.99.
a) What was the market yield rate on January 2?
b) What was the yield rate on September 28?
c) What was the rate of return realized?
Q4) You purchase a 182-day treasury bill for $240,000 at a rate of 3.546%. What did you sell it for 111 days before maturity if the new interest rate is 3.778%?
A) $238220.20
B) $238320.20
C) $238200.20
D) $238100.20
E) $241469.24
Q5) Find the maturity value of a $473 note issued on October 4 at 8.5% for 190 days. To view all questions and flashcards with answers, click on the resource link above. Page 11
Chapter 9: Compound Interest - Future Value and Present Value
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Sample Questions
Q1) If $3000.00 is invested for seven years and seven months at 6% p.a. compounded quarterly, calculate the maturity value.
A) $3763.18
B) $3776.32
C) $4745.43
D) $4712.57
E) $4882.57
Q2) You borrowed $1700.00 at 12.36% p.a. compounded monthly, and repaid $800.00 after three years and $950.00 after five years. How much do you owe at the end of the nine years?
Q3) You will need three amounts of $14,200 in each year for four years in order to go to school. You are planning on going to school starting in 5 years and ending in 8 years (years 5, 6, 7, 8). You are able to earn 9.64% compounded quarterly. How much money do you have to have today in order to be able to go to school?
A) $30574.35
B) $30457.35
C) $30754.35
D) $30475.34
E) $33354.35
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Chapter 10: Compound Interest - Further Topics
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Sample Questions
Q1) Calculate the nominal rate of interest compounded semi-annually that will double money in eight years.
Q2) In how many years will money triple at 12% compounded semi-annually?
Q3) Calculate the nominal annual rate of interest compounded quarterly that is equivalent to 10% p.a. compounded semi-annually.
Q4) In how many days will $770.00 grow to $880.00 at 11.5% p.a. compounded monthly?
Q5) If the effective rate of interest on an investment is 6.52%, what is the nominal rate of interest compounded monthly?
Q6) The treasurer of Lynn Lake Credit Union proposes changing the method of compounding interest on premium savings accounts to daily compounding. If the current rate is 4% compounded quarterly, what nominal rate should the treasurer suggest to the Board of Directors to maintain the same effective rate of interest?
Q7) If $1400.00 accumulates to $2350.00 in five years, six months compounded semi-annually, what is the effective rate of interest?
Q8) 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?
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Chapter 11: Ordinary Simple Annuities
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Sample Questions
Q1) What is the future value of an annuity with monthly deposits of $277 for a period of 11.5 years at an interest rate of 7.44% compounded monthly? The deposits are made at the end of the month.
A) $60616.68
B) $60161.68
C) $60186.68
D) $60611.68
E) $60001.68
Q2) Calculate the accumulated value of monthly payments of $100.00 made at the end of each month for ten years just after the last payment has been made if interest is 12% p.a. compounded monthly.
A) $23 003.87
B) $33 003.87
C) $12 000
D) $1 046.22
E) $330 003.87
Q3) What is the size of semi-annual deposits that will accumulate to $113 200.00 after 9.5 years at 6.5% compounded semi-annually?
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Chapter 12: Ordinary General Annuities
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Sample Questions
Q1) What sum of money can be withdrawn from a fund of $46 950.00 invested at 6.5% compounded semi-annually at the end of every three months for twelve years?
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) 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) What is the future value of payments of $230.00 made at the end of every three months in twenty-one years if interest is 7.65% compounded annually?
Q5) 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?
Q6) How much must be deposited at the end of each month for 10 years to accumulate to $100 000.00 at 6.00% compounded yearly?
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Chapter 13: Annuities Due, Deferred Annuities, and Perpetuities
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Sample Questions
Q1) Payments of $500.00 are made at the beginning of each month for four years. The interest rate is 4.5% compounded monthly. If no further deposits are made
a) Calculate the accumulated value twelve years after the first deposit.
b) Calculate the amount deposited.
c) Calculate the interest.
Q2) 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?
Q3) Slick Sean contributes $500.00 at the beginning of each month into RRSP paying interest at 6.00% compounded semi-annually. What will be the accumulated balance in the RRSP at the end of 15 years?
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Chapter 14: Amortization of Loans, Including Residential Mortgages
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Sample Questions
Q1) A debt of $42 500.00 is repaid by payments of $4850.00 made at the end of each year. Interest is 7% compounded semi-annually.
a) How many payments are needed to repay the debt?
b) What is the cost of the debt for the first three years?
c) What is the principal repaid in the 3rd year?
d) Construct an amortization schedule showing details of the first three payments, the last three payments, and totals.
Q2) A loan of $14 100.00 is amortized over 11 years by equal monthly payments at 5.4% compounded monthly. Construct an amortization schedule showing details of the first three payments, the fortieth payment, the last three payments, and totals.
Q3) A debt of $12 970.00 with interest at 7.23% compounded semi-annually is repaid by payments of $1880.00 made at the end of every three months. Construct an amortization schedule showing the total paid and the total cost of the debt.
Q4) Tom receives pension payments of $6000.00 at the end of every six months from a retirement fund of $90 000.00. The fund earns 8.00% compounded semi-annually.
a) How many payments will Tom receive?
b) What is the size of the final pension payment?
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Chapter 15: Bond Valuation and Sinking Funds
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Sample Questions
Q1) 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%
Q2) A $50 000, 4% bond with semi-annual coupons is purchased three years before maturity. Calculate the discount or premium if the bond is sold to yield 6% compounded semi-annually.
Q3) A 50 000 bond bears interest at 4.5% payable semi-annually and is redeemable at par on November 4, 2022. The bond is sold on March 20, 2013, to yield 5.5% compounded semi-annually. What is the cash price?
Q4) 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.
Q5) A $5000, 6.25% bond with interest payable annually redeemable at par in eight years is purchased to yield 7.5% compounded annually. Find the premium or discount and the purchase price and construct the appropriate bond schedule.
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Chapter 16: Investment Decision Applications
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Sample Questions
Q1) 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.
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 restaurant may be purchased for $250 000. Annual net income from the operation of the restaurant is expected to be $61 000 for each of the first 4 years and $30 000 for each of the next three years. After 7 years, the restaurant can be sold for $315 000. Determine the rate of return on the investment correct to the nearest tenth of a percent. a) Use linear interpolation to find the approximate value of the rate of return. b) Find the answer using Cash Flow and IRR.
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