Question

You are trying to calculate how much money you should have at retirement. On your 57 th birthday you will retire and immediately make your first withdrawal of ?$4166.67. You plan to make 24 such withdrawals each year. You plan to continue withdrawing at that level and frequency until you are 72 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 4.4?% per annum. How much do you have to have saved at retirement to fund these planned? withdrawals?

Answer #1

Amount of annual withdrawals = $4,166.67

Number of annual withdrawals = n = 24

Annual rate of interest = r = 4.4% = 0.044

The beginning of year withdrawals forms an annuity due and the amount required at the time of retirement shall be the present value of annual withdrawals after retirement

Present value of annuity due = Annuity amount + Annuity amount *
{1-(1+r)^{-(n-1)}}/r

Amount required at the time of retirement = $4,166.67 +
$4,166.67*(1-1.044^{-23})/0.044 = $63,689.46

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