Business Mathematics Exam
Preparation Guide
Course Introduction
Business Mathematics is a foundational course designed to equip students with the quantitative skills necessary for analyzing and solving problems in the business and finance sectors. The course covers key mathematical concepts such as algebra, linear equations, matrices, functions, calculus, and financial mathematics, including interest calculations, annuities, and amortization schedules. Emphasis is placed on practical applications in areas like accounting, economics, management, and marketing, enabling students to interpret and use mathematical data in decision-making, budgeting, forecasting, and strategic planning. Through lectures, problem-solving sessions, and real-world examples, students gain proficiency in mathematical reasoning relevant to business contexts.
Recommended Textbook
Contemporary Business Mathematics with Canadian Applications 9th Edition by S.
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A. Hummelbrunner
Chapter 1: Review of Arithmetic
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Sample Questions
Q1) Calculate the weighted-average cost of the following inventory purchases: Date
Quantity Purchased Cost per Unit Total Amount
June 4 30 $11.50 $345.00
June 14 40 $15.00 $600.00
June 29 30 $10.99 $329.70
A) $12.74
B) $12.75
C) $22.74
D) $22.75
E) $37.49
Answer: B
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) Simplify: 5(4 + 3)
Answer: 5 7 = 35
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Chapter 2: Review of Basic Algebra
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Sample Questions
Q1) An electronics company has been producing 1705 CD Players a day working two shifts. The second shift has produced 95 CD players fewer than four-fifths of the number of CD players produced by the first shift. Determine the number of CD players produced by the second shift.
Answer: Let the number of CD players produced by the first shift be x.
Number of CD players produced by the second shift = 11ea8930_32a6_82b1_b375_d18be8b044e7_TB4213_11 x - 95.
Total production = x + 11ea8930_32a6_a9c2_b375_6ba90ee19ffd_TB4213_11 x - 95 = 1705
x + 11ea8930_32a6_a9c3_b375_43811a35c406_TB4213_11 x - 95 = 1705
11ea8930_32a6_d0d4_b375_81ad7cfef436_TB4213_11 x = 1800 x = 1000
Production by the second shift is 11ea8930_32a6_d0d5_b375_17216d4a550c_TB4213_11 x(1000) - 95 = 705.
Q2) Simplify: 8(9y - 4) - 2(y - 1) - (1 - 3y)
Answer: 72y - 32 - 2y + 2 - 1 + 3y = 73y - 31
Q3) Simplify: 50xy ÷ (-5x)
Answer: -10y
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Page 4
Chapter 3: Ratio, Proportion, and Percent
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Sample Questions
Q1) Your earnings of $967.34 for the week represent 4.168% of your entire years earnings. What are your annualized earnings?
A) $23899.88
B) $23208.73
C) $28308.73
D) $22208.73
E) $28308.88
Answer: B
Q2) Calculate the cost of a $11 000.00 machine after a decrease of 5% in price.
Answer: New value is 11 000.00 - 11 000.00(0.05) = $10 450.00
Q3) Solve: 15:6 = 30:x
Answer: 15:6 = 30:x 11ea8930_32b3_7a7f_b375_213792490fca_TB4213_11 =
11ea8930_32b3_7a80_b375_8bee5f414859_TB4213_11 15x = (30)(6) x = 11ea8930_32b3_a191_b375_91deddf30da0_TB4213_11 x = 12
Q4) The number 675 is 37 1/2% more than what number?
Answer: 675 = x + 37.5% of x x + 11ea8930_32c5_556b_b375_fd4bcb813b62_TB4213_11 x = 675 = x + .375x 11ea8930_32c5_7c7c_b375_c3283bb7ac13_TB4213_11 x = 675 = 1.375x
11ea8930_32c5_7c7d_b375_fbdad93034d1_TB4213_11 x = x = 490.91
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Chapter 4: Linear Systems
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Sample Questions
Q1) Solve the system of equations: 6x + 5y = 30
4x - 3y = 24
Q2) Two brothers decide to invest in a vacant lot which cost $51000. The first brother contributes $1000 more than one-quarter of what the second brother contributes. How much does each brother contribute?
A) B1 = 11000, B2 =40000
B) B1 =40000, B2 =11000
C) B1 = 12500, B2 =38500
D) B1 = 50000, B2 =10000
E) B1 = 1000, B2 =50000
Q3) 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?
Q4) Find the slope and y-intercept: 1.5x + 3y = 2.4
Q5) Find the slope and y-intercept: 4x + 5y = 31
Q6) Graph: x + 4y = 8
Q7) Solve graphically: 4x = -2y and x = 6
Q8) Graph: 5x + 4y = 20
Page 6
Q9) Find the slope and y-intercept: 3x + 2y = 10
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Page 7
Chapter 5: Trade Discount, Cash Discount, Markup, and Markdown
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Sample Questions
Q1) A retailer buys a computer for resale at $500.00 less 35%, 10%. The store marks the merchandise to cover expenses of 15% of the regular selling price and a net profit of 24% of the regular selling price. During a clearance sale, the appliance is sold at a markdown of 25%. What is the operating profit or loss?
Q2) Mike's Suits and Accessories purchased men's shoes for $97.00 less 25.6%. The store operates at a normal gross profit of 25% of regular selling price. The owner marks all merchandise with new regular selling prices so that the store can offer a 20% discount. What is the new regular selling price?
Q3) DeSomma and Brown received an invoice for $14 520 dated November 29, terms 5/20, n/45, from Happy Valley Winery for a truckload of grapes received December 17. DeSomma and Brown made a partial payment of $4 955.00 on December 12.
a) By how much did DeSomma and Brown reduce the amount due on the invoice?
b) How much does DeSomma and Brown still owe?
Q4) An invoice for $6 200.00, dated May 28, 3/10, 1/20, n/60, was received on May 30. What payment must be made on June 5 to reduce the debt to $4760.00?
Q5) A gross profit of $96.00 is made on a sale. If the gross profit was 52% based on selling price, what was the cost?
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Chapter 6: Break-Even and Cost-Volume-Profit Analysis
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Sample Questions
Q1) A company that makes customized pens has calculated their revenue and costs as follows for the most recent fiscal period: Sales $100 000 Costs:
Fixed Costs $???????
Variable Costs 15 000
Total Costs ???????
Net Income (Loss) $(20 000)
What are the company's fixed costs per fiscal period?
A) $105 000
B) $115 000
C) $80 000
D) $85 000
E) $120 000
Q2) 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) 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) What principal will earn $77.14 interest at 6.65% p.a. for 182 days?
Q3) What principal will have a maturity value of $100 000 at 5% p.a. in 18 months?
Q4) Compute the amount of interest on $250.00 at 8.25% p.a. from March 30, 2014 to October 28, 2014.
Q5) What principal will earn $59.99 interest at 7.75% p.a. from February 4, 2014 to July 17, 2014?
Q6) Find the amount of interest on $635.00 at 6.5% p.a. from October 2, 2015 to August 4, 2016.
Q7) 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%?
Q8) A loan of $4100 is to be repaid in three equal installments due 110, 197, and 311 days respectively after the date of the loan. If the focal date is the date of the loan and interest is 6.89% p.a., find the size of the installments.
Q9) How many months will it take $639 to grow to $795 at 8.45% p.a.?
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Chapter 8: Simple Interest Applications
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Sample Questions
Q1) You bought a $100,000 91-day T-bill for $99453.67 61 days before maturity. What discount rate was used?
A) 3.29%
B) 2.39%
C) 3.49%
D) 4.39%
E) 3.99%
Q2) An investor purchased $250 000 in 91-day T-bills on the issue date for $248 157.56. After holding the T-bills for 37 days, she sold them for a yield of 3.25%.
a) What was the original yield of the T-bills?
b) For how much did the investor sell the T-bills?
c) What rate of return (per annum) did the investor realize while holding this T-bill?
Q3) 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%.
Q4) Determine the maturity value of a 120-day note for $2 260.00 dated May 9 and bearing interest at 5.66%.
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) Calculate the future value of $5000 if it is invested at an interest rate of 16% compounded quarterly for 5 years and 6 months.
A) $11849.59
B) $11809.59
C) $11049.59
D) $10849.59
E) $5849.59
Q2) How much would you have to deposit in an account today to have $37000.00 in a three-year term deposit at maturity if interest is 7.775% compounded annually?
Q3) What is the present value of $7800.00 payable in six years if the current interest rate is 7.6% p.a., compounded quarterly?
Q4) What is the cash value of $5 000 if it is discounted for 5 years at 10% compounded yearly?
A) $3100.61
B) $3000.61
C) $3143.28
D) $3228.43
E) $3104.61
Page 12
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Chapter 10: Compound Interest - Further Topics
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Q1) What is the nominal rate of interest compounded semi-annually that is equivalent to an effective rate of 8.25%
Q2) Calculate the effective annual rate for 5% p.a. compounded semi-annually.
A) 0.050625
B) 5.0625%
C) 0.0255%
D) 2.55%
E) 15.0625%
Q3) At what nominal rate of interest compounded semi-annually will $11 800 earn $6 800 interest in six years?
Q4) In how many days will $770.00 grow to $880.00 at 11.5% p.a. compounded monthly?
Q5) At what nominal rate of interest compounded semi-annually will $5900 earn $6400 interest in six years?
Q6) In how many years will money double at 6.62% compounded semi-annually?
Q7) Calculate the nominal rate of interest compounded semi-annually that will double money in eight years.
Q8) Find the equated date at which two payments of $1600.00 due six months ago and $1850.00 due today could be settled by a payment of $4300.00 if interest is 9.48% compounded monthly.
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Chapter 11: Ordinary Simple Annuities
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Sample Questions
Q1) $1000.00 is deposited at the end of every month into an account earning 6.00% compounded monthly. If the balance in the account five years after the last deposit is to be $50 000.00, how many deposits are needed?
Q2) How much interest is included in the accumulated value of $250 paid at the end of every month for 5 years if the interest rate is 4.0% compounded monthly?
Q3) An installment contract for the purchase of a car requires payments of $570.60 at the end of each month for the next three years. Suppose interest is 11.8% p.a. compounded monthly.
a) What is the amount financed?
b) How much is the interest cost?
Q4) Suppose $726.56 is deposited at the end of every six months into an account earning 6.45% compounded semi-annually. If the balance in the account four years after the last deposit is to be $31 300.00, how many deposits are needed?
Q5) What is the term of a mortgage of $235 000.00 repaid by monthly payments of $2475.00 if interest is 7.55% compounded monthly?
Q6) 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) 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
Q2) What is the principal from which $279.00 can be withdrawn at the end of each month for 17.5 years if interest is 5.44% compounded quarterly?
Q3) You miss the 11th to 13th payments of a loan. The loan payments are $519.27 each month and the interest rate is 8.45% compounded annually. How much are you behind in your payments on the day that you miss the 13th payment?
A) $1658.40
B) $1586.40
C) $1568.40
D) $1508.40
E) $1458.40
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Page 15
Chapter 13: Annuities Due, Deferred Annuities, and Perpetuities
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Q1) Equal sums of money are withdrawn monthly from a fund of $33 000.00 for 15.25 years. If interest is 9% compounded monthly, what is the size of each withdrawal if the withdrawal is made at the beginning of each month?
Q2) Your child is currently six years old. When he turns 19 you want him to be able to withdraw $14700 per year in order to either travel or go to school for four years. If you are able to earn 6.62% compounded semi-annually for the entire time period, what is the single amount of the deposit three years from now that will ensure that your child is able to do this?
A) $28777.49
B) $28877.49
C) $27777.49
D) $27877.49
E) $29877.49
Q3) Aaron Perry bought an income property for $41 321.00 three years ago. He has held the property for the three years without renting it. If he rents the property now, what should be the size of the monthly payment due in advance be if money is worth 6.24% compounded monthly?
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Page 16
Chapter 14: Amortization of Loans, Including Residential
Mortgages
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Q1) How much interest is paid in total on a 1-year loan for $5000? The interest rate is 12 % compounded monthly and the payments are monthly.
A) $330.00
B) $333.88
C) $333.00
D) $300.88
E) $330.88
Q2) Sean and friends bought a property valued at $50000 for $5 000.00 down and a mortgage amortized over 10 years. The group makes equal payments due at the end of every three months. Interest on the mortgage is 6.00% compounded annually and the mortgage is renewable after five years.
a) What is the size of each quarterly payment?
b) What is the outstanding principal at the end of the five-year term?
c) What is the cost of the mortgage for the first five years?
d) If the mortgage is renewed for a further five years at 9% compounded semi-annually, what will be the size of each quarterly payment?
Q3) A loan of $10000.00 is repaid by quarterly payments of $1000.00 each at 12% compounded quarterly. What is the principal repaid by the 11th payment?
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Chapter 15: Bond Valuation and Sinking Funds
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Sample Questions
Q1) A $200 000.00, 6% bond with semi-annual coupons is redeemable at par. What is the purchase price of the bond six years before maturity to yield 8% compounded semi-annually?
Q2) Ten $10 000, 4% bonds with interest payable semi-annually and redeemable at par are purchased 18.5 years before maturity. Find the premium or discount and the purchase price if the bonds are bought to yield 7%.
Q3) What is the total increase in the 71st monthly deposit interval of a sinking fund that is for 14 years and the sinking fund earn 4.8% compounded monthly? The original principal was $250000.
A) $1883.94
B) $1383.94
C) $1333.94
D) $1888.94
E) $1880.94
Q4) Find the gain or loss on the sale without constructing a bond schedule for six $5000, 9.5% bonds with interest payable semi-annually redeemable at par bought twenty-one years before maturity to yield 10.5% compounded semi-annually. The bonds were sold three years later at 103.625.
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Chapter 16: Investment Decision Applications
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Sample Questions
Q1) An investment of $180 000 yields annual net returns of $27 700 for seven years. What is the rate of return on the investment (correct to the nearest tenth of a percent) if part of the initial investment, in the amount of, $80 000 is recovered at the end of 7 years?
a) Use linear interpolation to find the approximate value of the rate of return.
b) Find the answer using Cash Flow and IRR.
Q2) 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.
Q3) Sean and Jessica want to sell their interest in a small business. They have received two offers. If they accept Offer A they will receive $40 000 immediately and $30 000 in two years. If the accept Offer B they will receive $50000 now and $2000 at the end of every six months for 5 years. If interest is 8%, which offer is preferable?
Q4) A special chemical development project requires an immediate outlay of $110 000 and $50 000 at the end of each year for 3 years. Net returns are nil for the first 3 years and $60 000 per year thereafter for fourteen years. What is the net present value of the project at 17%?
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