Question

The company you work for will deposit $400 at the end of each month into your retirement find. Interest is compounded monthly. You plan to retire in 15 years from now and estimate that you will need $2,000 per month out of the account for the next 10 years following your retirement. If the account pays 7.25% compounded monthly, how much do you need to put into the account in addition to your company deposit in order to meet your objective? Use TVM function on financial calculator (N, I/Y, PV, PMT, FV)

Answer 1

Solution:

The problem requires the use of both the present value and future value concepts in finance. Also, since the equal payments are made over equal intervals, we have to use the annuity formula:

PV of annuity = P x (1 - (1 + i)^-n) / i

FV of annuity = P x (1 + i)^n - 1) / i

where:

P = Periodic payment

i = interest rate

n = number of periods

According to the problem statement, you want to withdraw $2000 per month during retirement, which will last 10 years. In order for you to withdraw $2000 per month for 10 years, you need to compute how much money you should have in your retirement fund at the start of your retirement (15 years from now). This requires you to compute the present value of $2000 per month for 10 years. Using the formula for the PV of the annuity:

P = $2000 per month

i = 7.25% / 12 months = .60% per month

n = 10 years x 12 months per year = 120 months

PV of annuity = $2000 x (1 - (1 + 0.60%)^-120) / 0.60%

PV of annuity = $170,356.24 --> This is the amount that you need to have in your retirement fund when you reach your retirement age.

Money accumulated by depositing $400 every (At end of 15 Years)
Using future value of annuity formula

= P x (1 + i)^n - 1) / i

= 400*(((1 + .06)^180 - 1) /.06) = $129,577.23

The addition amount that need to be deposited

= $170,356.24 - $129,577.23

= $40,779.01