FUNCTIONS AND CHANGE COMBO
FUNCTIONS AND CHANGE COMBO
6th Edition
ISBN: 9781337801287
Author: Crauder
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter P, Problem 15E

The Rule of 72 This is a continuation of Exercise 14. Financial advisors sometimes use a rule of thumb known as Rule of 72 to get a rough estimate of the time it takes for an investment to double in value. For an investment that is compounded yearly at an interest rate of r % , this rule says it will take about 72 / r years for the investment to double. In this calculation, r is the integer interest rate rather than a decimal. Thus, if the interest rate is 8 % , we would use 72 / 8 rather than 72 / 0.08 .

For the remainder of this exercise, we will consider an investment that is compounded yearly at an interest rate of 13 % .

a. According to the Rule 72, how long will it take the investment to double in value?

Parts b and c of this exercise will check to see how accurate this estimate is for this particular case.

b. Using the answer you got from part a of this exercise, calculate the future value interest factor (as defined in Exercise 14). Is it exactly the same as your answer to the part a of Exercise 14?

c. If your initial investment was $ 5000 , use your answer from part b to calculate the future value. Did your investment exactly double?

Future Value Business and finance texts refer to the value of an investment at a future time as its future value. If an investment of P dollars is compounded yearly at an interest rate of r as a decimal, then the value of the investment after t years is given by

F u t u r e   V a l u e = P × 1 + r t .

In this formula, 1 + r t is known as the future value interest factor, so the formula above can be written as

F u t u r e   V a l u e = P × F u t u r e   v a l u e   i n t e r e s t   f a c t o r

Financial officers normally calculate this (or look it up in a table)

a. What future value interest factor will make an investment double?

b. Say you have an investment that is compounded yearly at a rate of 9 % .

Find the future value interest factor for a 7-year investment.

c. Use the results from part b to calculate the 7-year future value if your initial investment is $ 5000 .

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Chapter P Solutions

FUNCTIONS AND CHANGE COMBO

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