Math

a kind benefactor sets up a prize in an international school. the benefactor donates $10 000. the school invests the money in an account paying 5% interest. if $750 was paid out annually, for how long can the full prize be given out?

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  1. The present value An of the annuity=10,000

    An=p*(1-(1+i)^-n)/i

    10000=750*(1-1.05^-n)/0.05
    500=750*(1-1.05^-n)
    2/3=1-1.05^-n
    1.05^-n=1/3
    1.05^n=3
    n=ln3/ln1.05=22.51708531

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