Question

Cincinnati Company has decided to put $30,000 per quarter in a pension fund. The fund will earn interest at the rate of 8% per year, compounded quarterly. Find the amount available in this fund after 10 years.

Answer 1

Formula for future value of Annuity :
FV= A [ {(1+k)n-1}/k]
FV = Future annuity value
A = periodical investment
K=interest rate
N=periods

Now interest rate is 8% annual compounded quarterly
Say the nominal interest rate is r
r=n*[(1+i)^1/n-1]
where n =no of compounding periods =4
i=effective interest rate per yesr=8%
r= 4*(1.08^0.25-1)
r=7.77%
So nominal quarterly interest rate=7.77%/4=		=			1.9425%
Now fro FV of annuity formula
given A=	$            30,000	per qtr
k=1.9425%
n=40 quarters
FV= 30000*[(1.019425)^40-1]/0.019425
FV=	$1,789,643
So the amount available after 10 years will be $1,789,643