After winning the lottery, you are indifferent between receiving $750,000 end-of-the-year payments for 15 years or a lump-sum payment of $7,106,223 today. At what interest rate would you be
Indifferent between the two options?

Question

Quizplus · Accepted Answer

To find the interest rate that makes the lottery winner indifferent between the two options, we can use the present value formula:

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

Where PV is the present value of the end-of-the-year payments, PMT is the annual payment, r is the interest rate, and n is the number of years.

For the first option, we have:

PV = 750,000 x (1 - (1 + r)^-15) / r

For the second option, we have:

PV = 7,106,223

Since the winner is indifferent between the two options, we know that the present values must be equal:

750,000 x (1 - (1 + r)^-15) / r = 7,106,223

Solving for r using a financial calculator or software, we get r = 6.38%.

Therefore, the best choice would be to take the lump-sum payment of $7,106,223 today.

After Winning the Lottery, You Are Indifferent Between Receiving $750,000