You decide to open a retirement account at the local bank that pays 8%/yr/month.

Question

You decide to open a retirement account at the local bank that pays 8%/yr/month. For the next 20 years, you will deposit $400/month into the account, with all deposits and withdrawals occuring 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 account will occur on the day exactly 12 months after the last deposit.

a) What monthly withdrawal can you make if you want the account to last 15 yrs?

b) what montly withdrawl can you make if you want the account to last forever (with infinte withdrawls)

Explanation / Answer

a) future value of deposits after 20 years = 400*((1+.08/12)^240 - 1)/(.08/12) = 235608.2

let monthly withdrawl = A

A*(1-(1+.08/12)^-180)/(.08/12) = 235608.2

A = 2251.59/month

b) for perpetuity

A/(.08/12) = 235608.2

A = 1570.72/month for last forever

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