Your uncle has $300,000 invested at 7.5%,and he now wants to retire.He wants to withdraw $35,000 at the beginning of each year,beginning immediately.He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account.For how many years can he make the $35,000 withdrawals and still have $25,000 left in the end?

Question

Quizplus · Accepted Answer

To solve this problem, we can use the present value of an annuity formula:

PV = PMT * ((1 - (1/ (1 + r)^n)) / r)

where PV is the present value, PMT is the payment amount, r is the interest rate per period, and n is the number of periods.

We want to solve for n, given that the present value is $25,000, the payment amount is $35,000, and the interest rate is 7.5%.

$25,000 = $35,000 * ((1 - (1/ (1 + 0.075)^n)) / 0.075)

Simplifying this equation gives:

0.7143 = (1 - (1/(1 + 0.075)^n))

Solving for n using logarithms gives:

n = 13.27

Therefore, your uncle can make the $35,000 withdrawals for 13.27 years, and still have $25,000 left in the end. The closest answer choice is C) 13.27.

Your Uncle Has $300,000 Invested at 7