aunt has $500,000 invested at 5.5%, and she now wants to retire.She wants to withdraw $45,000 at the beginning of each year, beginning immediately.She also wants to have $50,000 left to give you when she ceases to withdraw funds from the account.What is the maximum number of $45,000 withdrawals that she can make and still have at least $50,000 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

We can use the formula for the present value of an annuity to solve this problem. Let A be the annual withdrawal of $45,000, r be the annual interest rate of 5.5%, and n be the number of years of withdrawals. Then we can set up the equation:

500,000 = A*((1 - (1+r)^(-n))/r) + 50,000*(1+r)^(-n)

Simplifying this equation, we get:

45000*((1 - (1+0.055)^(-n))/0.055) = 45000*n + 50,000

Dividing both sides by 45,000, we get:

((1 - (1+0.055)^(-n))/0.055) = n/20 + 10/9

We can then use trial and error to find the maximum integer value of n that satisfies this equation. Starting with n = 13, we get:

LHS = 13.155
RHS = 13.45

So n = 13 does not work. Trying n = 14, we get:

LHS = 14.171
RHS = 14.45

So n = 14 works. Therefore, the maximum number of withdrawals she can make and still have at least $50,000 left in the account is 14.

Aunt Has $500,000 Invested at 5