You have $1,500 to invest today at 7% interest compounded annually. a. Find how

Question

You have $1,500 to invest today at 7% interest compounded annually.
a. Find how much you will have accumulated in the account at the end of
(1) 3 years, (2) 6 years, and (3) 9 years.
b. Use your findings in part a to calculate the amount of interest earned in
(1) the first 3 years (years 1 to 3), (2) the second 3 years (years 4 to 6),
and (3) the third 3 years (years 7 to 9).
c. Compare and contrast your findings in part b. Explain why the amount of
interest earned increases in each succeeding 3-year period.

Explanation / Answer

Future value = P×(1+r)^n

P is present value

r is interest rate per period

n is number of periods

a)

For 3 years:

= $1,500×(1+7%)^3

= $1,837.56

For 6 years:

= $1,500×(1+7%)^6

= $2,251.10

For 9 years:

= $1,500×(1+7%)^9

= 2,757.69

b)

Interest for 1-3 years:

= $1,837.56-$1,500

= $337.56

Interest for 4-6 years:

= $2,251.10-$1,837.56

= $413.54

Interest for 7-9 years:

= $2,757.69-$2,251.10

= $506.59

c)

Because of compounding effect of interest, interest earned in each set of period is increasing.

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