Question

16. How much money will I need to have at retirement so I can withdraw $60,000 a year for 20 years from an account earning 8% compounded annually? 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?

Answer 1

• starting balance: $636,215.95
• total withdrawals: $1,200,000
• interest withdrawn: $563,784.05

Explanation:

a) If we assume the annual withdrawals are at the beginning of the year, we can use the formula for an annuity due to compute the necessary savings.

The principal P that must be invested at rate r for n annual withdrawals of amount A is ...

P = A(1+r)(1 -(1 +r)^-n)/r

P = $60,000(1.08)(1 -1.08^-20)/0.08 = $636,215.95

__

b) 20 withdrawals of $60,000 each total ...

20×$60,000 = $1,200,000

__

c) The excess over the amount deposited is interest:

$1,200,000 -636,215.95 = $563,784.05