You have just won the Powerball lottery. The prize is $5,000,000 which is to be
ID: 2707437 • Letter: Y
Question
You have just won the Powerball lottery. The prize is $5,000,000 which is to be received in equal payments over 20 years, with the first payment beginning today. Assume an interest rate of 7% over the 20 years. Did you actually win $5,000,000? If not, what did you actually win? Rigorously support your answer.
You have just won the Powerball lottery. The prize is $5,000,000 which is to be received in equal payments over 20 years, with the first payment beginning today. Assume an interest rate of 7% over the 20 years. Did you actually win $5,000,000? If not, what did you actually win? Rigorously support your answer.Explanation / Answer
Hi,
Please find the answer as follows;
This is a case of annuity due. You need to calculate the present value of annuity due in this case.
Nper = 20
Rate = 7%
FV = 0
PMT = 5000000/20 = 250000
Type = 1
PV = ?
Present Value = PV(Rate,Nper,PMT,FV,Type) = PV(7%,20,250000,0,1) = 2833898.81 or 2833899
The present value of all the annuity payments over a period of 20 year turns out to be 2833899 which is less than the lottery prize money 5000000.
The amount actually won = 2833898.81 or 2833899
Thanks.
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