Question

several years ago the Wall Street Journal reported that the winner of the Massachusetts state lottery prize had the misfortune to be both bankrupt and in prison for fraud. The price was $9,420,713 to be paid in 19 equal annual installments. (There were 20 installments, but the winner had already received the first payment.) The bankruptcy court judge ruled that the prize should be sold off to the highest bidder and the proceeds used to pay off the creditors. If the interest rate was 8%, how much would you have been prepared for the prize ?

Answer 1

To calculate how much to pay for a lottery prize paid in 19 annual installments at an 8% interest rate, one would use the present value of annuity formula. The calculation requires knowing the annual payment, interest rate, and remaining number of payments to find the maximum price that would yield at least an 8% return on the investment.

Step-by-step explanation:

The student asked how much one would be prepared to pay for a Massachusetts state lottery prize of $9,420,713 to be paid in 19 equal annual installments at an interest rate of 8%. To determine the present value of the annuity (the lottery prize), we would use the formula for the present value of an annuity considering the interest rate and the number of payments left. When payments are made at the end of each period, the present value of annuity formula is used: PV = Pmt x [(1 - (1 + r)^{-n}) / r], where PV is the present value of the annuity, Pmt is the annual payment, r is the annual interest rate (as a decimal), and n is the number of payments remaining.

Since one payment has been made, there are 19 payments remaining, each of the amount $9,420,713 / 20. The interest rate is 8% or 0.08 in decimal form. Given this information, we calculate the present value of this annuity. Although the exact calculation is not provided here, this operation would provide the maximum amount one should pay if you want to make sure your investment yields at least an 8% return.