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math

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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? $

  • math - ,

    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

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