Course Introduction
Mathematics of Finance
Chapter Exam Questions
Mathematics of Finance provides students with a foundational understanding of quantitative techniques used in financial decision-making. The course covers topics such as simple and compound interest, annuities, amortization, bond pricing, and an introduction to risk and return. Emphasizing problem-solving and real-world application, students learn how mathematical models are utilized to value financial instruments, analyze investment strategies, and measure financial risk. This course is essential for students interested in finance, economics, actuarial science, or any field requiring financial analysis skills.
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) Yanping receives a monthly salary of $1 931.54 paid semi-monthly. The regular workweek is 38 hours.
a) Calculate the hourly rate of pay.
b) If the gross earnings for one pay period is 1 270.75, for how many hours of overtime was Yanping paid at double-time regular pay.
Answer: a) Annual gross earnings = 1931.54 × 12 = 23 178.48
Weekly gross earnings = 11ea8930_327e_fd99_b375_dba43b31ac0c_TB4213_11 = 445.74
Hourly rate of pay = 11ea8930_327e_fd9a_b375_29f1572dda84_TB4213_11 = $11.73
b) Regular semi-monthly gross earnings = 11ea8930_327f_24ab_b375_0398ed6392e5_TB4213_11 = 965.77
Overtime pay = 1270.75 - 965.77 = 304.98
Overtime rate = 11.73 × 2 = 23.46
Overtime hours = 11ea8930_327f_4bbc_b375_55fbf5e8d5ba_TB4213_11 = 13 hours
Q2) Evaluate: 395(2 + .15 290/365)
Answer: 395 * (2 + .15 .7945205) = 395 (2 + .1191781) = 395 (2.1191781) = 837.075
Q3) Simplify: 9(8 - 5) + 5(6 + 4)
Answer: 9 3 + 5 10 = 27 + 50 = 77
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Page 3
Chapter 2: Review of Basic Algebra
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Sample Questions
Q1) Express in logarithmic form: 39 = 19683
Answer: 9 = log3 19683
Q2) Simplify: (21x - 36) ÷ (-3)
Answer: -7x + 12
Q3) Evaluate: m<sup>0</sup>
Answer: 1
Q4) Simplify: -(3m - 6m - 5) - (4 - 7m - 2m)
Answer: -3m + 6m + 5 - 4 + 7m + 2m = 12m + 1
Q5) Simplify: -(4 - 6a) - (-8 + 6a)
Answer: -4 + 6a + 8 - 6a = 4
Q6) Solve: 5(8x - 2) - 5(3x + 5) = 36
Answer: 5(8x - 2) -5(3x + 5) = 36
40x - 10 -15x - 25 = 36
25x - 35 = 36
25x = 71
x = 2.84
Q7) Evaluate: (1.05)<sup>0</sup>
Answer: 1
Q8) Express in logarithmic form: 56 = 19683
Answer: 6 = log5 15625
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Chapter 3: Ratio, Proportion, and Percent
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Sample Questions
Q1) A manufacturing process requires $68.5 supervision cost for every 64 labor hours. At the same rate, how much supervision cost should be budgeted for 18 000 labor hours?
Answer: Let the supervision cost for 18000 hours be $x. 11ea8930_32bb_b834_b375_b779ab8d2771_TB4213_11 =
11ea8930_32bb_df45_b375_b522ccd2a63c_TB4213_11 64x = 68.5 18000
64x = 1233000
x = $19265.63
Q2) Overhead cost of a fan belt is three-eighths of total cost and labour cost is one-third of overhead cost. If labour cost is $15, what is the total cost of the fan belt?
Answer: Let overhead cost be $x. 11ea8930_32bf_fe0d_b375_f77ee3b73d02_TB4213_11 = 11ea8930_32bf_fe0e_b375_57271f922fd9_TB4213_11 , x = 45
Let the total cost be $y. 11ea8930_32c0_251f_b375_dd81fddb16e5_TB4213_11 = 11ea8930_32c0_2520_b375_efbd506c1749_TB4213_11 , 3y = 8(45), y = 120
Total cost is $120
Q3) 63 is what percent of 45?
Answer: Rate = 11ea8930_32c1_3696_b375_4d015334e19a_TB4213_11 = 1.4 = 140%
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5
Chapter 4: Linear Systems
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Sample Questions
Q1) Solve graphically: x - y = 4 and x + y = 6
Q2) Solve the system of equations: 5x = 10 - 2y
5y = 3x - 30
Q3) Solve graphically: 4x = -2y and x = 6
Q4) Find the slope and y-intercept: 3y - 5 = 2(x - 2)
Q5) It takes a car 10 seconds to increase its speed from 60 k/hr to 90 k/hr. What is the rate of acceleration (slope) in k/hr/sec?
A) 6
B) 9
C) 3
D) 1/6
E) 1/9
Q6) Find the y-intercept for the following: 3x - 5y = 60
A) 12
B) -12
C) 60
D) -60
E) -5
Q7) Solve the system of equations: 6x + 5y = 30
4x - 3y = 24
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Chapter 5: Trade Discount, Cash Discount, Markup, and Markdown
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Sample Questions
Q1) 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?
Q2) Christine's pet shop buys cat litter for $15.00 less 20% per bag. The store's overhead is 45% of cost and the owner requires a profit of 20 % of cost.
a) For how much should a bag be sold?
b) Calculate the amount of markup.
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) Find the cost of a car sold for $25 000 to realize a markup of 8% based on cost.
Page 7
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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) 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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8
Chapter 7: Simple Interest
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Sample Questions
Q1) What rate of interest is paid if the interest on a loan of $15 000.00 is $2 000.00 from January 31, 2014 to May 31, 2014?
Q2) An appliance store advertises a stove for $747.50 with nothing down, no payments and no interest for six months. Determine the cash value the store would be willing to accept if on a six-month investment, it can earn an interest of 4%.
Q3) Daniel's credit card statement last month showed $560 in cash advances and $5.25 in interest charges. The interest rate on the statement was 18.8%. For how many days was Daniel charged interest?
Q4) What rate of interest did you earn for a period of 2417 days if you invested $175 and you earned $222 in interest?
A) 16.19%
B) 17.19%
C) 29.19%
D) 21.19%
E) 19.16%
Q5) Compute the accumulated value of $6 500.00 at 8.5% after eleven months.
Q6) What sum of money will accumulate to $1 426.80 in eight months at 7.78%?
Q7) Determine the deposit that must be made to earn $85 in 7 months at 10.5%.
Page 9
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Chapter 8: Simple Interest Applications
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Sample Questions
Q1) A $2850, five-month promissory note with interest at 6.15% is issued on June 1. Compute the proceeds of the note on August 13, when money is worth 7.5%.
Q2) 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%
Q3) You lend a friend $1300 on May 11th. The demand loan rate is 10.12%. Your friend makes a partial payment on May 26th for $550 and on June 19th for $675. You demand full repayment of the outstanding balance on July 17th. What is the final payment amount to? Use the declining balance method.
A) $68.10
B) $86.10
C) $88.10
D) $82.10
E) $96.10
Q4) 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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Q1) What sum of money will grow to $23000.00 in seven years at 9.612% compounded monthly?
Q2) 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.
Q3) Six years after Ellen deposited $4500 in a savings account that earned interest at 4.68% compounded monthly, the rate of interest was changed to 6.4% compounded semi-annually. How much was in the account thirteen years after the deposit was made?
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
Q5) What is the present value of $7800.00 payable in six years if the current interest rate is 7.6% p.a., compounded quarterly?
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Chapter 10: Compound Interest - Further Topics
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Sample Questions
Q1) In how many days will $770.00 grow to $880.00 at 11.5% p.a. compounded monthly?
Q2) How long, in compounding periods, will it take for $3327 to increase by $3799 if you are able to earn 6.2% compounded semi-annually?
A) 42.95
B) 24.95
C) 4.56
D) 6.45
E) 4.95
Q3) What is the monthly discount rate expressed as an nominal annual rate for a future value of $182500 to be reduced to $178,663.58 over a period of 4.25 years?
A) 4.06%
B) 8.04%
C) 6.88%
D) 4.88%
E) 0.50%
Q4) In how many months will money double at 7.45% compounded semi-annually?
Q5) What is the nominal rate of interest compounded semi-annually which is equivalent to an effective rate of 5.89%?
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Chapter 11: Ordinary Simple Annuities
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Q1) You currently have $4000 saved towards the purchase of a new car. You want to be able to buy a car for $15000 in 4 years. Your money is earning 5% compounded yearly. What is the size of your yearly deposit?
A) $928.05
B) $2320.12
C) $2552.13
D) $2352.13
E) $2000.99
Q2) 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
Q3) 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?
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Chapter 12: Ordinary General Annuities
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Q1) 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?
Q2) You buy a motorcycle for $52523 plus freight of $724 and other delivery charges of $561. You have saved 25% of the total purchase price towards a down payment. The bank is willing to finance the purchase of the motorcycle at 9.86% compounded quarterly. What is the size of your monthly payment if the loan is for 4.5 years?
A) $296.80
B) $926.80
C) $962.80
D) $996.80
E) $262.80
Q3) What is the principal invested at 6.76% compounded semi-annually from which monthly withdrawals of $450.00 can be made at the end of each month for 22 .75 years?
Q4) Note: The calculations for this question were done using Excel's RATE function.
What is the rate of interest compounded quarterly if a loan of $31 500.00 is repaid in seven years by payments of $2712.00 made at the end of every six months?
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Chapter 13: Annuities Due, Deferred Annuities, and Perpetuities
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Q1) 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
Q2) You bought a camper priced at $15 660.00 on February 1. You agreed to make monthly payments of $575.00 beginning December 1 of the same year. For how long will you have to make these payments if interest is 8.5% compounded monthly?
Q3) A debt of $140 000.00 is to be repaid in installments due at the end of each month for 15.5 years. If the payments are deferred for three years and interest is 7.28% compounded quarterly, what is the size of the monthly payments?
Q4) What deposit made at the beginning of each month will accumulate to $36 000.00 at 5% compounded quarterly at the end of eight years?
Page 15
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Chapter 14: Amortization of Loans, Including Residential
Mortgages
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Q1) A bank has an interest rate of 5% compounded semi annually for a five year closed mortgage. If the mortgage has monthly payments, calculate the effective rate of interest per each term.
Q2) A contract worth $59 000.00 provides benefits of $21 000.00 at the end of each year. The benefits are deferred for six years and interest is 8.95% compounded quarterly.
a) How many payments are to be made under the contract?
b) What is the size of the last benefit payment?
Q3) Barbara borrowed $12 000.00 from the bank at 9% compounded monthly. The loan is amortized with end-of-month payments over five years.
a) Calculate the interest included in the 20th payment.
b) Calculate the principal repaid in the 36th payment.
c) Construct a partial amortization schedule showing the details of the first two payments, the 20th payment, the 36th payment, and the last two payments.
d) Calculate the totals of amount paid, interest paid, and the principal repaid.
Q4) Payments of $1000.00 deferred for nine years are received at the end of each month from a fund of $20 000.00 deposited today at 6% compounded monthly. Calculate the size of the final payment.
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Chapter 15: Bond Valuation and Sinking Funds
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Q1) 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.
Q2) A $40 000.00, 5% bond with semi-annual coupons redeemable at par in 14 years is purchased to yield 7% compounded semi-annually. What is the gain or loss if the bond is sold three years before maturity at 99.75?
Q3) What is the amount of premium/discount for a bond that has 4 years till it matures? The face value of the bond is $100 000 and it has a bond rate of 6.4% compounded semi-annually. The bond is sold to yield 7.4% compounded semi-annually.
A) $3084.47
B) $3840.47
C) $3048.47
D) $3408.47
E) $3184.47
Q4) A $100 000, 8.75% bond with interest payable annually is redeemable at 103 in four years. What is the purchase price to yield 7% compounded quarterly?
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17
Chapter 16: Investment Decision Applications
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Q1) 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.
Q2) A company has the following pattern of cash flows. Today -$47000, Year 1 -$15500, Year 2 +$16000, Year 3 +$35000, Year 4 +$57000. What is the IRR?
A) 9.301%
B) 29.301%
C) 19.301%
D) 39.301%
E) 49.301%
Q3) 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.
Q4) You win a lottery and have a choice of taking $200 000.00 immediately or taking payments of $8000.00 at the end of every three months for ten years. Which offer is preferable if interest is 8% compounded quarterly?
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