John won a lottery that will pay him €200,000 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 formula for the present value of an annuity:

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

where:
PV = present value
C = cash flows per year (€200,000)
r = interest rate (8%)
n = number of periods (20 years)

Plugging in the values, we get:

PV = 200,000 * ((1 - (1+0.08)^-20) / 0.08)
PV = €1,963,630

Therefore, the present value of the lottery winnings is €1,963,630. Choice C is the best answer.

John Won a Lottery That Will Pay Him €200,000 at the End