Question

Withdrawal Amount, Over the years, Ahmed and Aamina El-zayaty, of Berkeley California, have accumulated $200,000 and $220,000, respectively, in their employer-sponsored retirement plans. If the amounts in their two accounts earn a 6 percent rate of return over Ahmed and Aamina's anticipated 20 years of retirement, how large an amount could be withdrawn from the two accounts each month? Use the Garman/Forgue companion website or Appendix A-4 to make your calculations.

Answer 1

To calculate the withdrawal amount, we need to use the Present Value of an Annuity (PVA) formula. The PVA formula is:

PVA = A x (1 - (1 + r)^-n) / r

Where:

A = the amount of the withdrawal each period

r = the interest rate per period

n = the number of periods

First, we need to calculate the total amount in the retirement accounts:

Total amount = $200,000 + $220,000 = $420,000

Next, we need to calculate the interest rate per period. Since the El-zayatys will be withdrawing money each month, we need to convert the annual interest rate of 6% to a monthly interest rate:

Monthly interest rate = 6% / 12 = 0.5%

Finally, we need to calculate the number of periods. Since the El-zayatys will be withdrawing money each month for 20 years, the total number of periods will be:

Number of periods = 20 x 12 = 240

Now we can plug in the values into the PVA formula:

PVA = A x (1 - (1 + r)^-n) / r

$420,000 = A x (1 - (1 + 0.005)^-240) / 0.005

Solving for A, we get:

A = $2,816.64

Therefore, the El-zayatys can withdraw $2,816.64 each month from their retirement accounts for 20 years if their accounts earn a 6% rate of return.