John won a lottery that will pay him $100,000 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

This is a case of an annuity with a fixed amount to be paid each year. We can use the formula for present value of an annuity to calculate the present value of the payments.

PV = Payment x ((1 - (1 + r)^-n) / r)

Where PV is the present value, Payment is the annual payment, r is the interest rate, and n is the number of years.

Plugging in the given values, we get:

PV = $100,000 x ((1 - (1 + 0.08)^-20) / 0.08)
PV = $981,815

Therefore, the present value of the 20-year annuity is $981,815.

John Won a Lottery That Will Pay Him $100,000 at the End