Marcus Jones wants to invest $10,000 on January 1, 2014, so that he may withdraw 10 annual payments of equal amounts beginning January 1, 2029. If the fund earns 10% annual interest over its life, what will be the amount of each of the withdrawals?
A) $10,000
B) $14,709
C) $16,181
D) $28,402

Question

Quizplus · Accepted Answer

To solve this, we use the formula for the present value of an annuity. First, we find the present value of the annuity on January 1, 2029, which is when the withdrawals start. The formula for the present value of an annuity is PV = PMT * [(1 - (1 + r)^-n) / r], where PMT is the payment amount, r is the interest rate per period, and n is the number of periods. However, since we're given the present value ($10,000) and need to find PMT, we rearrange the formula to solve for PMT. The $10,000 needs to be grown for the 15 years (2014 to 2029) at 10% to find the future value on January 1, 2029, which then serves as the present value for the annuity calculation. The future value is calculated as $10,000 * (1 + 0.10)^15 = $41,772.18. Then, using the annuity formula for PMT with n = 10 and r = 10%, we find PMT = $41,772.18 * [0.10 / (1 - (1 + 0.10)^-10)] = $16,181.

Marcus Jones Wants to Invest $10,000 on January 1, 2014