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8 September, 13:43

Kevin Morales invests $14,963.72 now for a series of $2,200 annual returns beginning one year from now. Kevin will earn a return of 6% on the initial investment. How many annual payments of $2,200 will Kevin receive?

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  1. 8 September, 17:13
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    Answer = 9 years

    Explanation:

    Present value of annuity=Annuity[1 - (1+interest rate) ^-time period]/rate

    14,963.72=2200[1 - (1.06) ^-n]0.06

    14,963.72=36,666.67[1 - (1.06) ^-n]

    1 - (1.06) ^-n = (14,963.72/36,666.67)

    (1.06) ^-n=1 - (14,963.72/36,666.67)

    (1/1.06) ^n=0.591898545

    Taking log on both sides;

    n*log (1/1.06) = log 0.591898545

    Hence n=log0.591898545/log (1/1.06)

    =9 years.
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