Question

A company deposited $5,500 into an investment fund at the beginning of every quarter for 5 years. It then stopped making deposits into the fund and allowed the investment to grow for 4 more years. The fund was growing at 4.25% compounded monthly.

a. What was the accumulated value of the fund at the end of 5 years ?

b. What was the accumulated value of the fund at the end of 9 years ?

c. What was the amount of interest earned over the 9-year period?

Answer 1

Effective quarterly rate, r = (1 + 0.0425/12)^3 - 1

r = 0.01066267463

a. n = 5 * 4 = 20 quarterly payments

r = 0.01066267463

PMT = 5,500

The accumulated value of the fund at the end of 5 years was $121,888.783916686

b. FV9 = FV5 * (1 + r)^n

n = (9 - 5) * 4 = 16 quarters between year 5 and 9

n = 16

r = 0.01066267463 per quarter

FV9 = 121,888.783916686 * (1 + 0.01066267463)^16

FV9 = 121,888.783916686 * 1.1849489188

FV9 = $144,431.9827159239

The accumulated value of the fund at the end of 9 years was $144,431.9827159239

c. Interest earned = The accumulated value of the fund at the end of 9 years - Quarterly payment * Number of payments

Interest earned = 144,431.9827159239 - 5,500 * 20

Interest earned = $34,431.9827159239

The amount of interest earned over the 9-year period was $34,431.9827159239