Question

Suppose David just won the state lottery, and you have a choice between receiving $3,000,000 today or a 20-year annuity of $250,000, with the first payment coming one year from today. What rate of return is built into the annuity? Disregard taxes.

A.
4.52%
B.
5.45%
C.
3.45%
D.
6.15%

Answer 1

The correct answer is B. 5.45%.

The rate of return built into the annuity is equal to the present value of the annuity divided by the initial amount, $3,000,000.

The present value of an annuity can be calculated using the formula PV = PMT [(1 - (1 / (1 + i)^n)) / i], where PMT is the payment amount, i is the rate of return, and n is the number of payments.

In this case, the PMT is $250,000, i is 5.45%, and n is 20, yielding a present value of $3,000,000.

Therefore, the rate of return is 5.45%.