Joe won a lottery jackpot that will pay him $12,000 each year for the next ten years. If the market interest rates are currently 12%, how much does the lottery have to invest today to pay out this prize to Joe over the next ten years?

 

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  • Let i be the annual interest rate. Let v=1/(1+i)
    Let A be the present value of the annuity.
    Let n be the number of years of payments.
    Let P be the annual payment.

    Then A = P*(1-v^n)/i

    i = 0.12
    n = 10
    P = 12,000
    v = 1/(1+i)=0.89286
    A = 12,000*(1-0.89286^10)/0.12 =
    67,801.65

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