Question

Michael plans to retire in 40 years. He is now trying to decide how much to save for his retirement. He plans to deposit equal amount at the beginning of each month in a retirement account for 40 years, with his first saving made today. Assume the retirement account pays him an interest rate of 6.6% p.a., compounded monthly and Michael would like to have $2,000,000 in his retirement account 40 years later

a)  How much will he have to deposit per month to accumulate $2,000,000 in 40 years?  [3 marks]

b)  If he hopes to live for 25 years in retirement, how much can he withdraw every month (starting one month after retirement) so that he will just exhaust his savings of $2,000,000 with the last withdrawal (assume his savings will continue to earn him 6.6% p.a. compounded monthly)?  [3 marks]

c)  If, instead he decides to withdraw $12,000 per month (again with the first withdrawal one month after retiring) for 25 years and leave the remaining account balance to his children, how much money will Michael be able to leave to his children?  

Answer 1

a) FV or Retirement fund =2000000
Rate per month =6.6%/12
Number of months =40*12 =480
Amount deposited per month using annuity due formula =FV/((1+r)*((1+r)^n-1)/r) =2000000/((1+6.6%/12)*((1+6.6%/12)^480-1)/(6.6%/12))=847.25

b) Number of Withdrawals =25*12 =300
Rate per month =6.6%/12
Amount of withdrawal =Retirement Fund/((1-(1+r)^-n)/r) =2000000/((1-(1+6.6%/12)^-300)/(6.6%/12)) =13629.38

c) Amount of withdrawal =12000
Rate per month =6.6%/12
Number of Withdrawals =25*12 =300
Amount of Money Michael will be able to leave to his children =Retirement Fund*(1+r)^n-PMT*((1+r)^n-1)/r)
=2000000*(1+6.6%/12)^300-12000*((1+6.6%/12)^300-1)/(6.6%/12)) =1239364.99