girlfriend just won the Florida lottery.She has the choice of $15,000,000 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?

Question

Quizplus · Accepted Answer

To determine the rate of return built into the annuity, we can use the present value formula: PV = PMT * (1 - (1+r)^-n)/r, where PV is the present value (which is equal to the $15,000,000 option), PMT is the annual payment ($1,050,000), r is the rate of return, and n is the number of years (20). Plugging in the given values, we get:

$15,000,000 = $1,050,000 * (1 - (1+r)^-20)/r

Solving for r using trial and error or a financial calculator, we get r = 3.44%. Therefore, the best choice for the girlfriend would be to take the $15,000,000 option today, as it has a higher present value than the annuity, and she can then invest the money herself to potentially earn a higher rate of return.

Girlfriend Just Won the Florida Lottery