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27 June, 12:49

What is the present value of a fund that earns 15% on its balance each year, from which $10,000 must be paid a year for 6 years, after which the balance of the fund will be zero?

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  1. 27 June, 13:10
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    The present value of the fund=$25,939.66

    Step-by-step explanation:

    Step 1

    Determine the future value of the fund as shown;

    Future value (F. V) = payment amounts per year*number of years

    where;

    payment amounts per year=$10,000

    number of years=6

    replacing;

    Future value (F. V) = (10,000*6) = 60,000

    Future value (F. V) = $60,000

    Step 2

    Determine the present value (P. V) of the fund as shown;

    F. V=P. V (1+r) ^n

    where;

    F. V=future value

    P. V=present value

    r=annual interest rate

    n=number of years

    In our case;

    F. V=$60,000

    P. V=unknown

    r=15%=15/100=0.15

    n=6

    replacing;

    60,000=P. V (1+0.15) ^6

    60,000=P. V (1.15) ^6

    P. V=60,000/{ (1.15) ^6}

    P. V=25,939.66

    The present value of the fund=$25,939.66
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