Question

Question 1 You decide to open a retirement account at your local bank that pays 7%/year/month (7% per year compounded monthly). For the next 20 years, you will deposit $400 per month into the account, with all deposits and withdrawals occurring at month’s end. On the day of the last deposit, you will retire. Your expenses during the first year of retirement will be covered by your company’s retirement plan. As such, your first withdrawal from your retirement account will occur on the day exactly 12 months after the last deposit.

What monthly withdrawal can you make if you want the account to last 25 years?

what monthly withdrawal can you make if you want the account to last forever (with infinite withdrawals)

Answer 1

Nominal interest rate = 7% annual compounding monthly

So, effective monthly interest rate R = 7% / 12

Monthly interest rate R = .5833%

Monthly deposit = $400

Time = 240 months

Future value at the end of 20 years = 400*((1+.5833%)^240 - 1)/.005833 = $ 208360.54

Since the withdrawal will be after 1 year.

Then,

Future value at the end of 21 years = 208360.54*(1+.5833%)^12 = $223422.05

If monthly withdrawal is done only for 25 years:

Let, monthly withdrawal is P.

Then,

223422.05 = P*(1-1/(1+.5833%)^300)/.005833

223422.05 = P*141.49

P = $1579.04

So, monthly withdrawal will be $1579.04 if it is to be done for 25 years.

If monthly withdrawal is on perpetuity basis.

Then,

Monthly withdrawal = 223422.05*.5833%

Monthly withdrawal = $1303.22