Question

You decide to open an individual retirement account (IRA) at your local bank that pays 8 %/year compounded annually. At the end of each of the next 40 years, you will deposit $4,000 into the account. Three years after your last deposit, you will begin making annual withdrawals. What annual amount will you be able to withdraw if you want the withdrawals to last:

A, 20 years? $

B, 30 year? $

C, Forever? $

Answer 1

Interest rate, r = 8% = 0.08

First, let's find the future value of our annual deposits as of one year before the first withdrawal. That is 42 years from now.

PMT = 4,000

n = 40

r = 0.08

A. We want the annual withdrawals to last for 20 years

n = 20

PV = 1,208,654.093693376

r = 0.08

We can withdraw $123,104.0891451778 per year for 20 years

B. We want the annual withdrawals to last for 30 years

n = 30

PV = 1,208,654.093693376

r = 0.08

We can withdraw $107,361.6409893887 per yer for 30 years

C. We want the annual withdrawals to last forever

PMT = PV * r

PMT = 1,208,654.093693376 * 0.08

PMT = $96,692.3274954701

We can withdraw $96,692.3274954701 per year forever

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