Question by needhelp: How much does the lottery have to pay out?
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?



Best answer:

Answer by fcas80
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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