Question

A newly-graduated engineer begins her job on her 24th birthday, and beings contributing to her retirement account the following month. Her company has agreed to match her contributions up to 4% of her salary, so she elects to contribute 4% to get the full company match (so the total contribution to the fund is 8%). Her starting monthly salary is $5000, and it’s expected to increase an average of 3% per year (or 0.25% per month). Her nominal annual MARR is 9%, compounded monthly.

A) If her salary increases an average of 3% per year (0.25% per month) and she works at the company until her 50th birthday, how much will be in the account at that time?

B) If she changes jobs, but keeps the money in her original account until she retires on her 65th birthday, how much will be in her account at that time? You can assume that her nominal annual MARR remains at 9% compounded monthly.

C) Based on your answer from (b), how much can she withdraw each month if she wants the money to last indefinitely (i.e., forever?) if she begins withdrawing from the account when she’s 65 (i.e., the month after her 65th birthday)? You can again assume a MARR value of 9% for the entire time span.

(if using excel please post code)

Answer 1

a) Her first payment, P = 5,000 x 8% = 400 including employer contribution. She will make 26 x 12 = 312 such payments till age 50.

Future value of the account can be calculated using FV formula

FV = P / (r - g) x [(1 + r)^n - (1 + g)^n]

where, P = 400, r = 9%/12 = 0.75%, g = 0.25%, n = 312,

=> FV = P / (0.75% - 0.25%) x [(1 + 0.75%)^312 - (1 + 0.25%)^312] = $648,931.10

b) Value at age 65, FV = PV x (1 + r)^n = 648,931.10 x (1 + 0.75%)^(12*15) = $2,490,625.64

c) Monthly withdrawal = Value x monthly rate = 2,490,625.64 x 0.75% = $18,679.69