You want to be able to withdraw $20,000 each year for 20 years. Your account earns 5% interest. a) How much do you need in your account at the beginning? b) How much total money will you pull out of the account? c) How much of that money is interest?

You want the amount required to support annual withdrawals of $20,000 for 20 years if the account earns 5%, and the amount of interest earned during the withdrawal period.

a) Present value

The present value of a withdrawal annuity is given by the formula ...

P = w(1 -(1 +r)^-t)/r

where w is the withdrawal amount, r is the interest rate per period, and t is the number of periods.

Here, that amounts to ...

P = 20,000(1 -(1 +0.05)^-20)/(0.05) ≈ 249,244.21

You need $249,244.21 in your account at the beginning.

b) Withdrawals

The 20 withdrawals will total ...

20 × $20,000 = $400,000

You will pull out a total of $400,000 from the account.

c) Interest

The amount that is interest will be the difference between the total withdrawn and the initial principal:

interest = $400,000 -249,244.21 = $150,755.79

About $150,755.79 of the amount withdrawn is interest.

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Additional comment

The formula used here assumes the withdrawals are at the end of each year, so the account earns interest for a year before the first withdrawal. If the withdrawals are at the beginning of the year, then the principal amount needs to be increased by 5%. The amount of interest withdrawn will be decreased accordingly.