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.

A. If he starts making these deposits in one year and makes his last deposit on the day he retires, what amount must he deposit annually to be able to make the desired withdrawals at retirement?

A1) First: Amount needed at retirement:

A2) The amount Dave must save each year (beginning at the end of the first year) to fund his retirement is:

A3) If Dave decides to make monthly deposits to reach his same retirement goal, how much must Dave start depositing one month from today?

Answer 1

Number of Years of Deposit = 36 years or (36 x 12) = 432 months, Planned Retirement Withdrawals = $ 125000, Retirement Tenure = 25 years and Interest Rate = 6.5 %

Amount Needed at Retirement = Sum of the Present Value of the Planned Retirement Withdrawals at the end of 36 years = 125000 x (1/0.065) x [1-{1/(1.065)^(25)}] = $ 1524734.591

Let the required annual deposits be $ k

Deposit Tenure = 36 years

Therefore, k x (1.065)^(35) + k x (1.065)^(34) +.................+ k = 1524734.591

k x [{(1.065)^(36)-1}/{(1.065)-1}] = 1524734.591

k x 133.096945 = 1524734.591

k = $ 11455.819 ~ $ 11455.82

Applicable Monthly Interest Rate = 6.5 / 12 = 0.54167 %

Let the required monthly deposits be $ m

Therefore, 1524734.591 = m x (1.0054167)^(431) + ...............+ m

m x [{(1.0054167)^(432) - 1}/{(1.0054167)-1}] = 1524734.591

m x 1719.873 = 1524734.591

m = $ 886.539 ~ $ 886.54