Martin has deposited $375 in his IRA at the end of each quarter for the past 20

Question

Martin has deposited $375 in his IRA at the end of each quarter for the past 20 years. His investment has earned interest at the rate of 8%/year compounded quarterly over this period. Now, at age 60, he is considering retirement. What quarterly payment will he receive over the next 15 years? (Assume that the money is earning interest at the same rate and that payments are made at the end of each quarter.) If he continues working and makes quarterly payments of the same amount in his IRA until age 65, what quarterly payment will he receive from his fund upon retirement over the following 10 years?

Explanation / Answer

Future value of IRA at end of 20 years = Present value of quarterly retirement payments over 15 years at 20 years from now

K = 20*4
Future value of annuity = [(375)*(1 +8/400)^K]    
k=1

   = 72664.484

K = N*4   
Present value of annuity = [(Future retirement payments)/(1 +discount rate/400)^k]     
k=1

K = 15*4   
72664.484 = [(Future retirement payments)/(1 +8/400)^k]     
k=1

Future retirement payments = 2090.4

Future value of IRA at end of 25 years = Present value of quarterly retirement payments over 10 years at 25 years from now   

K = 25*4
Future value of annuity = [(375)*(1 +8/400)^K]     
k=1

   = 117087.11

K = N*4   
Present value of annuity = [(Future retirement payments)/(1 +discount rate/400)^k]     
k=1

K = 10*4   
117087.11 = [(Future retirement payments)/(1 +8/400)^k]     
k=1

Future retirement payments = 4280.2

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