John won a lottery that will pay him $250,000 at the end of each of the next twenty years. Assuming an appropriate interest rate is 8% compounded annually, what is the present value of this amount?

Question

Quizplus · Accepted Answer

We can use the present value formula for an annuity (regular series of payments) to calculate the present value of John's lottery winnings.

PV = PMT * ((1 - (1 + r)^-n) / r)

Where PV is the present value, PMT is the payment per period, r is the interest rate per period, and n is the total number of periods.

In this case, PMT = $250,000, r = 8% per year (0.08), and n = 20 years.

PV = $250,000 * ((1 - (1 + 0.08)^-20) / 0.08) = $2,454,538

Therefore, the present value of John's lottery winnings is $2,454,538.

John Won a Lottery That Will Pay Him $250,000 at the End