Question

1. You are currently 25 years old, and while retirement is not the most pressing matter in your mind you have been thinking about it a lot lately. Specifically, you have heard from friends that it is never too early to begin saving for your retirement. So you open a retirement account with a balance of $0.00 that gives you an annual interest rate of 1.75% compounded monthly. You want to retire at age 65 with $1 million. How much will you need to deposit in the account each month to achieve that goal?

Answer 1

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

Monthly rate = Annual rate/ 12 months

                      = 1.75%/ 12 months

                      = 0.14583333333%

Hence, the monthly rate is 0.14583333333%.

The investment account starts at the age of 25 years and the age of retirement is 65 years. Thus the total period of monthly investment is 40 years. Hence, the number of monthly payments is 480.

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

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

                   = {1 – (1 + 0.0014583333333)^-480}/ 0.14583333333%

             = 345.024968489

Hence, the present value annuity factor is 345.024968489.

Compute the present value of the retirement fund, using the equation as shown below:

Present value = Retirement fund/ {(1 + Rate)^Time}

                      = $1,000,000/ {(1 + 0.0014583333333)^480}

                      = $1,000,000/ 2.01272611447

                      = $496,838.58763

Hence, the present value of the retirement fund is $496,838.58763.

Compute the monthly deposits, using the equation as shown below:

Monthly deposits = Present value/ PVIFA

                             = $496,838.58763/ 345.024968489

                             = $1,440.00763134

Hence, the monthly deposits are $1,440.00763134.