The winner of a "Fifty-million dollar" lottery prize is actually entitled to payments of $500,000 at the end of every six months for 50 years. The winner can select to receive a single lump sum payment equal to the present value of these payments calculated using a rate of 9.8% compounded semi-annually. What would be the amount of the single payment?
A) $5,101,597
B) $10,118,727
C) $20,118,147
D) $34,079,370
E) $39,453,072

Question

Quizplus · Accepted Answer

The single lump sum payment is the present value of an annuity. The formula for the present value of an annuity is PV = P * [(1 - (1 + r)^-n) / r], where P is the payment amount, r is the interest rate per period, and n is the total number of payments. Here, P = $500,000, r = 9.8% / 2 = 0.049 (since it's compounded semi-annually), and n = 50 * 2 = 100 (since payments are made every six months for 50 years). Plugging these values into the formula gives the present value, which is closest to option B, $10,118,727.

The Winner of a "Fifty-Million Dollar" Lottery Prize Is Actually