Bill Swill decides to try his luck at Powerball where the projected winnings are $12,000,000. If he wins, he can choose the annuity option (to be paid over 20 years) or a lump sum settlement that he can invest at 8% interest. How much must the lump sum option be to make the lump sum option equal to the annuity option (rounded)?
A) $2,574,578
B) $1,743,620
C) $1,130,668
D) $1,200,000

Question

Quizplus · Accepted Answer

To make the lump sum option equal to the annuity option, we need to calculate the present value of the annuity. The annuity pays $12,000,000 over 20 years, which is $600,000 per year. Using the formula for the present value of an annuity: PV = PMT × [(1 - (1 + r)^-n) / r], where PMT is the annual payment ($600,000), r is the annual interest rate (8% or 0.08), and n is the number of years (20). Plugging in these values gives us a present value of approximately $2,574,578, making the lump sum option equal to the annuity option when it is around this amount.

Bill Swill Decides to Try His Luck at Powerball Where