Mathematics for Business and Economics
Practice Questions
Course Introduction
Mathematics for Business and Economics introduces students to essential mathematical concepts and techniques used in analyzing and solving problems in business and economic contexts. The course covers topics such as linear equations, matrices, functions, financial mathematics (including interest and annuities), basic calculus (limits, derivatives, and integrals), and optimization methods. Emphasis is placed on practical applications, such as profit maximization, cost minimization, demand analysis, and resource allocation. Students will develop analytical skills and quantitative reasoning, enabling them to interpret data and make informed decisions in the fields of business and economics.
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) On a trip, a motorist purchased gasoline as follows: 66 liters at 69.0 cents per litre; 69 litres at 70.5 cents per litres; 80 litres at 71.5 cents per litre; and 57 litres at 74.5 cents per litre.
a) What was the average number of litres per purchase?
b) What was the average cost per litre?
c) If the motorist averaged 9.75 km per litre, what was her average cost of gasoline per kilometre?
Answer: a) 66 + 69 + 80 + 57 = 272
Average number of litres = 272 ÷ 4 = 68
b) Average cost per litre:
Total cost = 66 × 69.0 = 45.54
69 × 70.5 = 48.645
80 × 71.5 = 57.20
57 × 74.5 = 42.465
193.85 cents
Average cost = 193.86 ÷ 272 = 71.27 cents
c) Average cost per km = 71.27 ÷ 9.75 = 7.3097436 cents
Q2) Simplify: 3 + 8 4
Answer: 3 + 32 = 35
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Chapter 2: Review of Basic Algebra
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Sample Questions
Q1) Simplify: -(4 - 6a) - (-4 + 3a)
Answer: -4 + 6a + 4 - 3a = 3a
Q2) Simplify: (-64ab) ÷ (8ab)
Answer: -8
Q3) Simplify: -6m(-3m)
Answer: 18m2
Q4) Simplify: 4x - 3y - 4x - 2y
Answer: -5y
Q5) Compute: 32.5<sup>3/4</sup>
Answer: 13.611705
Q6) Simplify: (m<sup>5</sup>)5
Answer: (m<sup>5</sup>)<sup>5</sup> = m<sup>5×5</sup> = m<sup>25</sup>
Q7) Simplify: 60xy ÷ (-5xy)
Answer: -12
Q8) Express in logarithmic form: 39 = 19683
Answer: 9 = log3 19683
Q9) Evaluate: (-1)<sup>13</sup>
Answer: -1
Q10) Simplify: x + 0.16x
Answer: 1.16x
Page 4
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Page 5
Chapter 3: Ratio, Proportion,
and Percent
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Sample Questions
Q1) In the last provincial election, 62 1/2% of the population of 994 800 was eligible to vote. Of those eligible, 33 1/3% voted.
a) What was the number of eligible voters?
b) How many voted?
Answer: a) Number eligible = 62 11ea8930_32c4_43f0_b375_b719285609ae_TB4213_11 % of 994800
= 11ea8930_32c4_43f1_b375_c9d3f2bacb25_TB4213_11 x 994800 = 621,750
b) Number voting = 33 11ea8930_32c4_43f2_b375_69a01cdcd95a_TB4213_11 % of 621,750
= 11ea8930_32c4_6b03_b375_279be9412e25_TB4213_11 x 621,750 = 207,250
Q2) 27.5% of what amount is $28.63?
Answer: 27.5% of x = 28.63
.275x = 28.63
x = $104.11
Q3) What percent less than $90 is $81?
Answer: Decrease = 9
R = 11ea8930_32c5_0748_b375_25bfa365b2e7_TB4213_11 = .1 = 10%
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Chapter 4: Linear Systems
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Sample Questions
Q1) Find the y-intercept for the following equation: 5y + 7 = 19
A) 2.6
B) 0
C) 2.4
D) 2.8
E) 3.0
Q2) Graph: x = 5y
Q3) Solve the system of equations: x + 7y = 0 x + 4y = 8
Q4) Solve graphically: 4x = -2y and x = 6
Q5) Graph: y = -6
Q6) Find the slope and y-intercept: 4x + 5y = 31
Q7) Find the slope of the following: 2x + 5y = 50
A) .4
B) 2.5
C) -2.5
D) -.4
E) 10
Q8) Graph: x = -4
Q9) Graph: 3x - 2y = 18
7
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Chapter 5: Trade Discount, Cash Discount, Markup, and Markdown
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Sample Questions
Q1) 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%
Q2) Deep Discount Audio buys home theatre systems for $3 895 less 29%, 15%. Expenses are 30% of the regular selling price and the required profit is 41% of the regular selling price. All merchandise is marked with a new regular selling price so that the store can advertise a discount of 35% while still maintaining its regular markup. During the annual clearance sale, the new regular selling price of unsold items is marked down 40%. What operating profit or loss does the store make on items sold during the sale?
Q3) A hitch and trailer listed at $2 149.00 has a net price of $1 360.00. What is the rate of discount?
Q4) Find the cost of a car sold for $25 000 to realize a markup of 8% based on cost.
Page 9
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Chapter 6: Break-Even and Cost-Volume-Profit Analysis
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Sample Questions
Q1) 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?
Q2) 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
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Chapter 7: Simple Interest
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Sample Questions
Q1) A debt of $1410.00 due 6 months ago and a second debt of $1815.00 due in 4 months with interest at 6.16% p.a. are to be settled by two equal payments due now and 9 months from now respectively. Find the size of the equal payments at 7.37% p.a. with the agreed focal date now.
Q2) You owe $3572.75 in 147 days and have decided to pay off your loan early. Your interest rate is 6.52%. What is the size of the check that you write today to pay off all of your debt?
A) $4381.33
B) $3481.33
C) $3581.33
D) $3381.33
E) $3814.33
Q3) Calculate the amount of interest that will be charged on $7000.00 borrowed for five months at 5.5%.
Q4) What rate of interest is paid if the interest on a loan of $7300.00 is $692.71 from June 11, 2014 to April 2, 2015?
Q5) What is the present value of $9700.00 due at 6.25% p.a. in 89 days?
Q6) Determine the date represented by 100 days after March 1, 2012.
Q7) At what rate of interest will $1087.00 earn $63.84 in 264 days?
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Chapter 8: Simple Interest Applications
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Q1) Government of Manitoba 364-day T-bills with a face value of $2 000 000 were purchased on April 17 for $1 945 970. The T-bills were sold on May 25 for $1946 340.
a) What was the market yield rate on April 17?
b) What was the yield rate on May 25?
c) What was the rate of return realized?
Q2) Find the maturity value of a 60-day, 4% note for $3000 note dated February 25, 2011.
Q3) An investment dealer bought a 182-day Government of Canada treasury bill at the price required to yield an annual rate of return of 3.38%
a) What was the price paid by the investment dealer if the T-bill has a face value of $1 000 000?
b) Later the same day, the investment dealer sold this T-bill to a large corporation to yield 3.25%. What was the investment dealer's profit on this transaction?
Q4) Find the maturity value of a $473 note issued on October 4 at 8.5% for 190 days.
Q5) A 60-day non-interest-bearing promissory note for $10 000 is dated June 1, 2013. Compute the present value of the note on June 14, 2013, if money is worth 5%.
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Page 12
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
E) 1.8%
Q2) Four years and five months after its date of issue, a 7-year promissory note for $8900.00 bearing interest at 5.04% compounded monthly is discounted at 6.5% compounded semi-annually. Find the proceeds of the note using the exact method.
Q3) Payments of $10200.00 due one year ago and $13000.00 due nine months ago are to be replaced by a payment of $5800.00 now, a second payment of $10000.00 fifteen months from now, and a final payment twenty-four months from now. What is the size of the final payment if interest is 9.2% compounded quarterly?
Q4) Darcy's parents made a trust deposit of $3500.00 on October 31, 2002, to be withdrawn on Darcy's eighteenth birthday on July 31, 2016. To what will the deposit amount on that date at 13.48% compounded quarterly?
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Chapter 10: Compound Interest - Further Topics
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Q1) At what nominal rate of interest compounded quarterly will $ 13 000,00 earn $8407.27 in interest in six years? (nearest hundredth)
A) 1.83%
B) 2.10%
C) 7.33%
D) 8.4%
E) 18.4%
Q2) At what nominal rate of interest compounded semi-annually will $5900 earn $6400 interest in six years?
Q3) At what nominal rate of interest compounded quarterly will $2000.00 earn $400.00 interest in three years?
Q4) Determine the effective rate of interest corresponding to 6% p.a. compounded monthly
Q5) 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?
Q6) 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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Q1) What is the nominal rate of interest if a six-year loan of $71000.00 is repaid by monthly payments of $1701.58?
Q2) 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?
Q3) Annette bought a vacation property for $22900.00 down and quarterly mortgage payments of $1224.51 at the end of each quarter for six years. Interest is 8.4% compounded quarterly.
a) What was the purchase price of the property?
b) How much interest will Annette pay?
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 size of end-of-month monthly deposits which will accumulate to $122 200.00 after six years if interest is 5.7% compounded monthly?
Q6) Find the amount to which monthly deposits of $100.00 will grow in five years at 4.8% p.a. compounded monthly.
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Chapter 12: Ordinary General Annuities
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Q1) 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?
Q2) 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?
Q3) If a student loan was repaid by monthly payments of $800.00 in 5.0 years at 8.00% compounded yearly, how much interest was paid?
Q4) Calculate the nominal interest rate of interest compounded quarterly if a loan of 43 000.00 is repaid in seven years by payments of $4000.00 made at the end of every six months.
Q5) A 22-year mortgage is amortized by payments of $1761.50 made at the end of each month. If interest is 9.65% compounded semi-annually, what is the mortgage principal?
Q6) 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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Chapter 13: Annuities Due, Deferred Annuities, and Perpetuities
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Q1) 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.
Q2) Determine the accumulated value after 15 years of deposits of $500.00 made at the beginning of every 6 months and earning interest at 12% compounded monthly?
Q3) A contract valued at 60 000.00 requires payments of $3000.00 at the beginning of each quarter. If interest is 6% compounded quarterly, calculate the term of the contract.
Q4) Gibran bought a boat valued at $110 194.00 on the installment plan. He made equal semi-annual payments for 6 years. If the first payment is due on the date of purchase and interest is 7.5% compounded semi-annually, what is the size of the semi-annual payments?
Q5) Joshua deposited $3560.00 at the beginning of every 6 months for 11 years into a fund paying 3.5% compounded semi-annually. Fourteen years after the first deposit he converted the then existing balance into an annuity due paying him equal annual payments for 22 years. If interest for the annuity due is 5% compounded annually, what is the size of the annual payment?
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Chapter 14: Amortization of Loans, Including Residential
Mortgages
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Questions
Q1) How much interest is paid in total on a 3-year loan for $28600 (rounded to the nearest dollar)? The interest rate is 8.7% compounded monthly and the payments are monthly.
A) $3997
B) $3779
C) $3977
D) $3999
E) $4000
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 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.
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Chapter 15: Bond Valuation and Sinking Funds
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Q1) 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.
Q2) A $100 000, 8% bond with semi-annual coupons redeemable at par on April 25, 2018, was purchased on June 25, 2009, at 94.125. What was the approximate yield rate?
Q3) A 4.5% annuity bond of $500 000 with interest payable quarterly is to be redeemable at par in seven years.
a) What is the purchase price to yield 6% compounded quarterly?
b) What is the book value after 6 years?
c) What is the gain or loss if the bond is sold six years after the date of purchase at 99.625?
Q4) 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.
Q5) Twenty $5 000 bonds redeemable at par bearing 6% coupons payable quarterly are sold eight years before maturity to yield 5.5% compounded annually. What is the purchase price of the bonds?
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Chapter 16: Investment Decision Applications
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Q1) Replacing old office equipment at an immediate cost of $3 000 and $4 000 four years from now will result in savings of $400 semi-annually for ten years. Should the old equipment be replaced
a) at 8% compounded annually?
b) at 12% compounded annually?
Q2) A company spends $117 500 today and has positive cash inflows of $34 000 for each of the next 6 years. What is the Internal Rate of Return (IRR)?
A) 14.87%
B) 18.47%
C) 17.48%
D) 16.84%
E) 15.87%
Q3) 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%?
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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