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

The problem can be solved using the formula for the present value of an annuity and the future value of a lump sum. The uncle wants to withdraw $35,000 annually at a 7.5% interest rate and still have $25,000 left. First, calculate the present value of the $25,000 that he wants to leave behind, which is equivalent to having that amount in the account after the last withdrawal. The present value $PV$ of the future value $FV$ is calculated using the formula $PV = \frac{FV}{(1 + r)^n}$, where $r$ is the annual interest rate and $n$ is the number of periods. Then, add this present value to the annual withdrawal amount to find out how much the uncle needs initially to fulfill his plan. Finally, use the present value of an annuity formula to calculate the number of withdrawals $n$. Given the complexity of solving for $n$ directly due to the nature of the equation, financial calculators or spreadsheet software are typically used to find the precise number of periods. The correct answer is found by determining the maximum number of full $35,000 withdrawals that can be made while leaving at least $25,000 in the account, which aligns with option B, indicating 13 withdrawals. This approach combines understanding of financial formulas with practical application to retirement planning scenarios.

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