Question

You are planning to save for retirement over the next 40 years. To do this, you will invest $200 per month in a retirement account. The rate of return for the retirement account is expected to be 9 percent per year. After you retire, you expect that the account will have an annual return of 3 percent. How much can you withdraw each month from your account assuming a 25-year withdrawal period during retirement?

Answer 1

Compute the monthly interest rate before retirement, using the equation as shown below:

Monthly rate = Annual rate/ 12 months

                      = 9%/ 12 months

                      = 0.75%

Hence, the monthly rate is 0.75%.

Compute the present value annuity factor (PVIFA), using the equation as shown below:

PVIFA = {1 – (1 + Rate)^-Number of periods}/ Rate

                   = {1 – (1 + 0.0075)^-480}/ 0.75%

             = 129.640902011

Hence, the present value annuity factor is 129.640902011.

Compute the value of deposits at the time of retirement, using the equation as shown below:

Value of deposits = Monthly deposits*PVIFA*{(1 + Rate)^Time}

                             = $200*129.640902011*{(1 + 0.0075)^480}

                             = $25,928.1804022*36.1099020441

                             = $936,264.054505

Hence, the value of deposits is $936,264.054505.

Compute the monthly interest rate after retirement, using the equation as shown below:

Monthly rate = Annual rate/ 12 months

                      = 3%/ 12 months

                      = 0.25%

Hence, the monthly rate is 0.25%.

Compute the present value annuity factor (PVIFA), using the equation as shown below:

PVIFA = {1 – (1 + Rate)^-Number of periods}/ Rate

                   = {1 – (1 + 0.0025)^-300}/ 0.25%

             = 210.87645334

Hence, the present value annuity factor is 210.87645334.

Compute the monthly withdrawal amount, using the equation as shown below:

Monthly withdrawal = Value of deposits at the time of retirement/ PVIFA

                                  = $936,264.054505/ 210.87645334

                                  = $4,439.87007404

Hence, the monthly withdrawal amount is $4,439.87007404.