Question

Your best friend Dave just celebrated his 24th birthday and wants to start saving for his anticipated retirement. Dave plans to retire in 36 years and believes that he will have 25 good years of retirement and believes that if he can withdraw $125,000 at the end of each year, he can enjoy his retirement. Assume that a reasonable rate of interest for Dave for all scenarios presented below is 6.5% per year. This is an annual rate, review each individual question for more specifics on compounding periods per year. Because Dave 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.

B. If Dave decides instead to take exotic vacations each year for the next 5 years, and delay putting aside funds for that time, (1st deposit at the end of 5 years from now, leaving only 31 years to grow his retirement nest egg), what amount must he deposit annually to be able to make the desired withdrawals at retirement?

Answer 1

Kitty size required at the time of retirement should be good enough to lead to a year end withdrawal of 125,000 for the next 25 years at interest rate of 6.5% per year.

Hence, kitty size required at the time of retirement = PV (Rate, Nper, PMT, FV) = PV (6.5%, 25, -125000, 0) = $1,524,735

Since the first deposit start after the end of year 5, he will make n = 36 - 5 + 1 = 32 deposits.

Hence, FV of 32 annual deposits of say an amount A should be equal to the kitty size at the time of requirement.

Hence, A / r x [(1 + r)ⁿ - 1] =  $1,524,735

Hence, A / 6.5% x [(1 + 6.5%)³² - 1] = 1,524,735

100.03A = 1,524,735

Hence, amount he must deposit annually to be able to make the desired withdrawals at retirement = A = 1,524,735 / 100.03 = $15,242.24 (Please do round it off as per your requirement)