Djer invests $5000 each year into a mutual fund earning 6.15% compounded annually. After 8 years he stops making payments, but leaves the funds invested for an additional 4 years.
a) What is the value of the fund at the end of 8 years? $
b) What is the value of the fund after an additional 4 years? $
For an annual payment P for n years at interest rate r, the value of the investment is
A=Pr^n+Pr^(n-1)+....Pr
=Pr(1+r+r²+...+rn-1)
=Pr(rn-1)/(r-1)
After 8 years
P=5000
r=1.0615
n=8
A=5000*1.0615*(1.0615^8-1)/(.0615)
=52814.48
For the next 4 years
A=52814.48*1.0615^4
=67055.28