A lottery winner receives a $100 000 cheque now, and a second one in two years. If the annual interest rate is 9 percent, the present value of his total winnings is

Question

Quizplus · Accepted Answer

First, we need to calculate the present value of the second cheque that will be received in two years. Using the formula for present value of a single sum:
PV = FV / (1 + r)^n
where PV is the present value, FV is the future value, r is the interest rate, and n is the number of years.

PV of second cheque = 100,000 / (1 + 0.09)^2
PV of second cheque = $82,644.63

Now, we can find the total present value of the winnings by calculating the present value of the first cheque and adding it to the present value of the second cheque:
PV of total winnings = 100,000 + 82,644.63
PV of total winnings = $182,644.63

Therefore, the closest answer choice is A, $184,168.

A Lottery Winner Receives a $100 000 Cheque Now, and a Second