You are trying to calculate how much money you should have at retirement. On you

Question

You are trying to calculate how much money you should have at retirement. On your

51st

birthday you will retire and immediately make your first withdrawal of

$5,000.00.

You plan to make

26

such withdrawals each year. You plan to continue withdrawing at that level and frequency until you are

78

years old. (Assume beginning of period withdrawals with the first withdrawal on your retirement date and no withdrawal on your final birthday.) During retirement your savings will earn only

4.5%

per annum. How much do you have to have saved at retirement to fund these planned withdrawals?

How much do you have to have saved at retirement to fund these planned withdrawals?

Explanation / Answer

Total number of withdrawals = 26

We need to find the present value of the future withdrawals made at the beginning of the period

PV of annuity due = P*[(1-(1+r)^(-n)) / r] * (1+r)

P - Periodic payment = 5000

r - rate per period = 0.045

n - number of periods = 26

PV of annuity due = 5000*((1-(1+0.045)^(-26)) / 0.045) * (1+0.045) = 79141.04

Savings required at retirement = $79141.04

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