Cincinnati Company has decided to put $30,000 per quarter in a pension fund. The fund will earn interest at the rate of 6% per year, compounded quarterly. Find the amount available in this fund after 10 years.

Cincinnati Company has decided to put $30,000 per quarter in a pension fund. The fund will earn interest at the rate of 6% per year, compounded quarterly. Find the amount available in this fund after 10 years. 

Answer

Solution

monthly rate of interest  = 6%/4 = 0.015

Number of months = 10 x4 = 40

S = 30,000 (1.015)^40 + 30,000  (1.015)^39+ …….+30,000 (1.015)

Here , a=30,000 (1.015)^40 and x = 1/1.015

FV = 30,000 (1.015)^40 [1-(1/1/1.015^40)] / 1-1/1.015

Now, 1/1.015^40 = 1.015^-40 (Simple math)

FV = 30,000 (1.015)^40 [1-1.015^-40]/1-1.015^-1

FV = 1,652,457