Your uncle has $300,000 invested at 7.5%, and he now wants to retire.He wants to withdraw $35,000 at the end of each year, beginning at the end of this year.He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account.What is the maximum number of $35,000 withdrawals that he can make and still have at least $25,000 left in the account? (Hint: If your solution for N is not an integer, round down to the nearest whole number.)

Question

Quizplus · Accepted Answer

This problem can be solved using the formula for the present value of an annuity: $PV = PMT \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)$, where PV is the present value (initial investment), PMT is the annual withdrawal amount, r is the annual interest rate, and n is the number of payments. Rearranging to solve for n, and considering the future value that needs to remain ($25,000), we adjust the equation to account for this by subtracting the future value discounted back to the present value from the initial investment. Using trial and error or financial calculators and plugging in the given values ($300,000 initial investment, 7.5% interest rate, $35,000 withdrawal), we find that the maximum number of $35,000 withdrawals that can be made while still leaving at least $25,000 in the account is 13.

Your Uncle Has $300,000 Invested at 7