Your uncle has $340,000 invested at 7.5%,and he now wants to retire.He wants to withdraw $35,000 at the end of each year,starting 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.For how many years can he make the $35,000 withdrawals and still have $25,000 left in the end?

Question

Quizplus · Accepted Answer

Using the formula for the present value of an annuity:
PV = (PMT / r) x (1 - (1 + r)^-n)
where PV is the present value, PMT is the payment, r is the interest rate, and n is the number of payments.

We can solve for n to find how many years he can withdraw $35,000 and still have $25,000 left over.
$25,000 = ($35,000 / 0.075) x (1 - (1 + 0.075)^-n) + ($35,000 / 0.075) x (1 + 0.075)^-n
$25,000 = $466,666.67 x (1 - (1 + 0.075)^-n) + $466,666.67 x (1 + 0.075)^-n
Simplifying and solving for n using a financial calculator or spreadsheet, we get:
n = 18.75

Therefore, the answer is B) 18.75.

Your Uncle Has $340,000 Invested at 7