Question

Your best friend Frank just celebrated his 30th birthday and wants to start saving for his anticipated retirement. Frank plans to retire in 35 years and believes that he will have 20 good years of retirement and believes that if he can withdraw $90,000 at the end of each year, he can enjoy his retirement. Assume that a reasonable rate of interest for Frank for all scenarios presented below is 8% per year. This is an annual rate, review each individual question for more specifics on compounding periods per year. Because Frank is planning ahead, the first withdrawal will not take place until one year after he retires. he wants to make equal annual deposits into his account for his retirement fund.

Suppose your friend has just inherited a large sum of money. Rather than making equal annual payments, he has decided to make one lump sum deposit today to cover his retirement needs. What amount does he have to deposit today?

Answer 1

Amount required on the day of retirement is equal to the present value of future withdrawals

= 90,000*PVAF(8%, 20 years)

= 90,000*9.818

= $883,620

Amount required to be deposited today = 883,620/(1.08)³⁵

= $59,763.23

Hence, lump sum deposit today = $59,763.23