Question

Robert expects to make 24 monthly deposits of $360 into an investment account that earns 7.3% compounded quarterly. After a one year investment pause, he intends to take out 20 equal monthly amounts from his investment account, the first withdrawal being exactly one year from the date of his last deposit. What is the dollar amount of each withdrawal assuming after the last one he has drained his investment account to zero. Assume the account earns the same rate of interest stated above throughout the investment horizon.

Answer 1

Using formula

We know r=((1+7.3%/4)^(4/12)-1)*12=7.2560%

Accumulated value after 24 deposits=360/(r/12)*((1+r/12)^24-1)

Accumulated value after 1 year from last deposit=360/(r/12)*((1+r/12)^24-1)*(1+r/12)^12

Withdrawal=Accumulated value*(r/12)/(1-1/(1+r/12)^20)*1/(1+r/12)=360/(r/12)*((1+r/12)^24-1)*(1+r/12)^12*(r/12)/(1-1/(1+r/12)^20)*1/(1+r/12)=527.23

Hence, Monthly withdrawals=527.23

Using Excel

enter the below formula

=PMT((1+7.3%/4)^(4/12)-1,20,FV((1+7.3%/4)^(4/12)-1,12,0,FV((1+7.3%/4)^(4/12)-1,24,-360,0)),0,1)
=527.23