Question

An individual has saved $500,000 for retirement. He wants to receive quarterly payments for twenty years beginning three months from now. If the investment earns 12% compounded quarterly, determine the size of the payments he can receive. ($16,555.87) Cannot use Excel!

Answer 1

Answer : Calculation of Periodic Withdrawal :

Periodic Receipt = Present Value of annuity / { [1 - (1+r)^-n ] / r }

Where,          

Present Value of Annuity = 500,000

r is rate per period i.e   ==> 12% / 4 = 3% or 0.03 (Divided by 4 as compounded quarterly)

N is number of payments ==> 20 * 4 = 80 (Multiplied by 4 as compounded quarterly)

Periodic Receipt = 500,000 / { [1 - (1+0.03)^-80 ] / 0.03 }

= 500,000 / {[ 1 - 0.0939771] / 0.03}

= 500000 / 30.2007634

= 16555.87