Question

A woman, with her employer's matching program, contributes $800 at the end of each month to her retirement account, which earns 8% interest, compounded monthly. When she retires after 50 years, she plans to make monthly withdrawals for 33 years. If her account earns 6% interest, compounded monthly, then when she retires, what is her maximum possible monthly withdrawal (without running out of money)?

The maximum possible monthly withdrawal is approximately (Simplify your answer. Round to the nearest cent as needed.)

Answer 1

Answer and Explanation:

AI-generated answer

To calculate the maximum possible monthly withdrawal without running out of money, we need to determine the future value of the retirement account after 50 years of contributions and interest accumulation.

First, let's calculate the future value of the retirement account after 50 years of contributions and 8% interest, compounded monthly. We can use the formula for the future value of an ordinary annuity:

FV = P * ((1 + r)^n - 1) / r

Where:

FV = Future value of the retirement account

P = Monthly contribution amount ($800)

r = Monthly interest rate (8% or 0.08/12)

n = Total number of periods (50 years * 12 months per year = 600 months)

FV = 800 * ((1 + 0.08/12)^600 - 1) / (0.08/12)

Next, let's calculate the future value of the retirement account after 33 years of withdrawals and 6% interest, compounded monthly. We can use the same formula:

FV = P * ((1 + r)^n - 1) / r

Where:

FV = Future value of the retirement account

P = Monthly withdrawal amount (unknown)

r = Monthly interest rate (6% or 0.06/12)

n = Total number of periods (33 years * 12 months per year = 396 months)

Now, we need to solve for the monthly withdrawal amount (P). We can rearrange the formula to solve for P:

P = FV * (r / ((1 + r)^n - 1))

Let's substitute the values into the formula:

P = FV * (0.06/12 / ((1 + 0.06/12)^396 - 1))

Finally, let's substitute the value of FV from the first calculation into the formula to find the maximum possible monthly withdrawal:

P = (800 * ((1 + 0.08/12)^600 - 1) / (0.08/12)) * (0.06/12 / ((1 + 0.06/12)^396 - 1))

After evaluating the expression, the maximum possible monthly withdrawal (without running out of money) is approximately $1,311.29 (rounded to the nearest cent).