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

The value of the prize is the present value of the 19 equal annual installments.

Each equal annual installment = prize money / 20 =  $9,420,713 / 20 = $471,035.65

(There are 20 equal annual installments in total, however only 19 will be received by you, since 1 is already paid to the winner).

PV of annuity = P * [1 - (1 + r)^-n] / r,

where P = periodic payment

r = interest rate per period

n = number of periods

Here, P = equal annual installment, which is $471,035.65

r = annual interest rate, which is 8%

n = number of years, which is 19.

PV of annuity = $471,035.65 * [1 - (1 + 0.08)^-19] / 0.08,

PV of annuity = $4,523,637.59

You would be prepared to pay $4,523,637.59 for the prize