Question 1

An investor's portfolio increased in value by 53% over a five-year period while the Consumer Price Index rose from 121.6 to 135.3. What was the portfolio's annually compounded real rate of return?

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Question 2

To the nearest day, how long will it take a $20,000 investment to grow to $22,000 (including the accrued interest) if it earns 7% compounded quarterly? Assume that a quarter-year has 91 days.

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Question 3

A bank offers a rate of 5.0% compounded semiannually on its four-year GICs. What monthly compounded rate should the bank offer on four-year GIC's to make investors indifferent between the alternatives?

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Question 4

If the Consumer Price Index rose from 109.6 to 133.8 over an 8½-year period, what was the equivalent compound annual inflation rate during the period?

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Question 5

Which of the following rates would you prefer for a loan: 7.6% compounded quarterly, 7.5% compounded monthly, or 7.7% compounded semiannually?

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Question 6

A $10,000 investment grew to $12,000 after 39 months of semiannual compounding. What effective rate of return did the investment earn?

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Question 7

Rounded to the nearest month, how long will it take money to lose one-third of its purchasing power if the annual inflation rate is 3%?

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Question 8

Terry was supposed to pay $800 to Becky on March 1. At a later date, Terry paid Becky an equivalent payment in the amount of $895.67. If they provided for a time value of money of 8% compounded monthly, when did Terry make the payment?

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Question 9

The home the Bensons purchased 13 years ago for $115,000 is now appraised at $385,000.
What has been the annual rate of appreciation of the value of their home during the 13- year period?

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Question 10

If a company's annual sales grew from $165,000 to $485,000 in a period of eight years, what has been the compound annual rate of growth of sales during the period?

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Question 11

When discounted to yield 9.5% compounded quarterly, a $4500 four-year promissory note bearing interest at 11.5% compounded semiannually was priced at $5697.84. How long after the issue date did the discounting take place?

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Question 12

An investor paid $4217.17 to purchase a $10,000 face value strip bond for her RRSP. At this price the investment will provide a return of 6.47% compounded semiannually. How long (to the nearest day) after the date of purchase will the bond mature? Assume that each half-year is exactly 182 days long.

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Question 13

A credit union pays 5.25% compounded annually on five-year compound interest: GICs. It wants to set the rates on its semiannually and monthly compounded GICs of the same maturity so that investors will earn the same total interest. What should be the rates on the GICs with the higher compounding frequencies?

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Question 14

If an invoice indicates that interest at the rate of 1.2% per month will be charged on overdue amounts, what effective rate of interest will be charged?

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Question 15

To the nearest month, how long will it take an investment to double in value if it earns 7.5% compounded semiannually?

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Question 16

What is the time remaining until the maturity date of a $50,000 strip bond if it has just been purchased for $20,822.89 to yield 5.38% compounded semiannually until maturity?

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Question 17

If the nominal rate of interest paid on a savings account is 3% per annum compounded monthly, what is the effective rate of interest paid?

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Question 18

Maxine found an old pay statement from nine years ago. Her hourly wage at the time was $13.50 versus her current wage of $20.80 per hour. At what equivalent (compound) annual rate has her wage grown over the period?

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Question 19

If an interest rate of 6.9% compounded semiannually is charged on a car loan, what effective rate of interest should be disclosed to the borrower?

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Question 20

The population of a mining town declined from 17,500 to 14,500 in a five-year period. If the population continues to decrease at the same compound annual rate, how long, to the nearest month, will it take for the population to drop by another 3,000?

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Quiz 9: Compound Interest: Further Topics and Applications