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.For how many years can he make the $35,000 withdrawals and still have $25,000 left in the end?
A)14.96
B)15.71
C)16.49
D)17.32

Question

Quizplus · Accepted Answer

To solve this, we use the formula for the present value of an annuity and the present 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. The present value (PV) of the annuity (withdrawals) plus the present value of the lump sum ($25,000) should equal the initial investment ($300,000). The formula for the present value of an annuity is PV = P * [(1 - (1 + r)^-n) / r], where P is the payment, r is the interest rate per period, and n is the number of periods. The present value of the lump sum is calculated as FV / (1 + r)^n, where FV is the future value. By setting up the equation and solving for n, we find that the closest number of years he can make the withdrawals and still have $25,000 left is approximately 14.96 years.

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