Your girlfriend just won the florida lottery. she has the choice of $13,800,000 today or a 20-year annuity of $1,050,000, with the first payment coming one year from today. what rate of return is built into the annuity? disregard taxes.

a. 3.77%

b. 4.38%

c. 3.90%

d. 4.03%

e. 4.12%

The answer is b. 4.38%

An annuity that is worth $13,800,000.00 today, that lasts 20 time periods and pays a constant $1,050,000.00 over each time period has an interest rate of 4.38%.

Explanation:

With a 4.38% interest rate, the present value of the payments is lower than the future value. Thus, the $1,050,000.00 you will be receiving in orderly payments is worth less today than it will be tomorrow. This condition is consistent with the time value of money, which states that with time money appreciates rather than depreciates. In other words, if you invest the $1,050,000.00 payment, its value over 20 time periods will increase.