Question

William deposited $7,000 into a fund at the end of every quarter for 9 years. He then stopped making deposits into the fund and allowed the investment to grow for 4 more years. The fund was growing at a rate of 5.00% compounded monthly a. What was the accumulated value of the fund at the end of 9 years? $0.00 Round to the nearest cent b. What was the additional accumulated value of the fund in the last 4 years?

Answer 1

Answer a.

Quarterly deposit = $7,000
Number of deposits = 36 (9 years)

Annual interest rate = 5.00%
Monthly interest rate = 0.41667%

Effective annual rate = (1 + Monthly interest rate)^12 - 1
Effective annual rate = (1 + 0.0041667)^12 - 1
Effective annual rate = 1.05116 - 1
Effective annual rate = 0.05116 or 5.116%

Quarterly interest rate = (1 + Effective annual rate)^(1/4) - 1
Quarterly interest rate = (1 + 0.05116)^(1/4) - 1
Quarterly interest rate = 1.01255 - 1
Quarterly interest rate = 0.01255 or 1.255%

Accumulated value = $7,000*1.01255^35 + $7,000*1.01255^34 + … + $7,000*1.01255 + $7,000
Accumulated value = $7,000 * (1.01255^36 - 1) / 0.01255
Accumulated value = $7,000 * 45.157495
Accumulated value = $316,102.47

Answer b.

Time period = 4 years or 16 quarters

Accumulated value = $316,102.47 * 1.01255^16
Accumulated value = $385,914.89

Additional accumulated value = $385,914.89 - $316,102.47
Additional accumulated value = $69,812.42