A state lottery commission pays the winner of the Million Dollar lottery 40 inst

Question

A state lottery commission pays the winner of the Million Dollar lottery 40 installments of $25,000/year. The commission makes the first payment of $25,000 immediately and the other n = 39 payments at the end of each of the next 39 years. Determine how much money the commission should have in the bank initially to guarantee the payments, assuming that the balance on deposit with the bank earns interest at the rate of 9%/year compounded yearly. Hint: Find the present value of the annuity. (Round your answer to the nearest cent.)

Explanation / Answer

Hi,

Please find the detailed answer as follows:

Nper = 39 (indicates the number of annual payments)

Rate = 9% (indicates interest rate)

PMT = 25000 (indicates the amount of annual payment)

FV = 0 (indicates future value, if any)

PV = ? (indicates present value)

Present Value = PV(Rate,Nper,PMT,FV) = PV(9%,39,25000,0) = $2638138.07

Total Balance = Initial Payment + Present Value of 39 Payments = 25000 +2638138.07 = $2663138

Answer is $2663138.

Thanks.

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