math
posted by ms guzman on .
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^(n1)+....Pr
=Pr(1+r+r²+...+r^{n1})
=Pr(r^{n}1)/(r1)
After 8 years
P=5000
r=1.0615
n=8
A=5000*1.0615*(1.0615^81)/(.0615)
=52814.48
For the next 4 years
A=52814.48*1.0615^4
=67055.28