Question

Gwen just hit the lottery jackpot. She can either receive her winnings as $0.5 million per year for the next 25 years, or a single payment of $20 million right now. If Gwen expects to earn 6.5% annual interest on her investments, which option is better and by how much in present value terms?

a) The annuity, by $1.96 million
b) The annuity, by $9.44 million
c) The single payment, by $7.50 milion
d) The single payment, by $67.11 million
e) The single payment, by $13.90 million

Answer 1

To determine which option is better, we need to calculate the present value of the annuity and the single payment. Using the given interest rate, the present value of the annuity is $7.50 million and the present value of the single payment is $13.90 million. Therefore, the annuity option is better by $6.40 million in present value terms.

Step-by-step explanation:

To determine which option is better, we need to calculate the present value of the annuity and the single payment. Since Gwen expects to earn 6.5% annual interest on her investments, we can use the formula for calculating present value of an annuity: PV = PMT * ((1 - (1 + r)^-n) / r), where PV is the present value, PMT is the annual payment, r is the interest rate, and n is the number of years. Using this formula, the present value of the annuity is $7.50 million.

To calculate the present value of the single payment, we can use the formula: PV = FV / (1 + r)^n, where FV is the future value and n is the number of years. Using this formula, the present value of the single payment is $13.90 million. Therefore, the option of receiving $0.5 million per year for the next 25 years is better by $6.40 million in present value terms.