Question

A company deposited $9,500 into an investment fund at the beginning of every quarter for 4 years. It then stopped making deposits into the fund and allowed the investment to grow for 6 more years. The fund was growing at 3.50% compounded monthly.

a. What was the accumulated value of the fund at the end of 4 years ?

b. What was the accumulated value of the fund at the end of 10 years ?

c. What was the amount of interest earned over the 10-year period?

Answer 1

Effective annual rate = (1 + r / n)^n - 1
= (1 + 3.50%/12)^12 - 1
= 3.5567%

Quarterly interest rate = (1 + EAR)^(1/4) - 1
= (1 + 3.5567%)^(1/4) - 1
= 0.87755%

a)
Rate = 0.87755%
Nper = 4 * 4 = 16
PMT = $9,500
PV = 0

Accumulated value can be calculated by using the following excel formula:
=FV(rate,nper,pmt,pv,beginning of the period)
=FV( 0.87755%,16,-9500,0,1)
= $163,851.13

Accumulated value of the fund at the end of 4 years = $163,851.13

b)
Accumulated value of the fund at the end of 10 years = PV * (1 + r)^n
= $163,851.13 * (1 + 0.87755%)^(6*4)
= $202,077.76

Accumulated value of the fund at the end of 10 years = $202,077.76

c)
Total interest earned = Accumulated value of the fund at the end of 10 years - (Quarterly deposit * number of periods)
= $202,077.76 - ($9500 * 16)
= $202,077.76 - $152,000
= $50,077.76

Total interest earned = $50,077.76