A state lottery gives a winner the choice of receiving the winning amount in equ
ID: 2742149 • Letter: A
Question
A state lottery gives a winner the choice of receiving the winning amount in equal monthly payments for 20 years or receiving a lump sum equal to the present value of an annuity with future value equal to the winnings. The winner selecting monthly payments will receive $5,000,000/240 = $20,833.33 each month for each million dollars of winnings. (Round your final answers to two decimal places.)
(a) Find the present value of an annuity with monthly payments of $20,833.33, at an interest rate of 4.9% for 20 years, for the winner who wants a lump-sum payment.
$
(b) In order for the lottery to be more profitable, it is decided to pay the winnings in equal monthly payments for 25 years. Find the monthly payments of $5 million in winnings.
$
Find the present value of an annuity with those monthly payments at 4.9% for 25 years.
Explanation / Answer
A)Monthly rate = 4.9/12 = .40833%
Months =20*12 =240
Present value = PVAF@.40833%,240 * Annuity
= 152.8 * 20833.33
= $ 3,183,332.82
b)Monthly payment =Amount /Number of months
= 5,000,000 /(25*12)
= 5,000,000 / 300
= 16666.67
Present value = PVAF@.40833%,300 * Annuity
= 172.78*16666.67
= $ 2,879,666.67
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