Question

Dad has $25,000 in his 401k account and contributes 5% of his salary ever year. His employer will match up to 10% dollar for dollar. He currently has 100% of his 401k invested in the fixed rate fund earning 2%. How much money will dad have after 30 years when he is going to retire? Dad, 35, is an electrical engineer and earns $60,000 per year working for a local aerospace company. He has been getting a 3% raise every year.

Answer 1

Assume that starting salary is 60,000. Then, at the end of year 1, salary will be 60,000*(1+annual increase)

= 60,000*(1+3%) = 61,800. Out of the annual salary, 5% is put in the 401k. So, amount deposited = 5%*61,800 = 3,090

10% of this amount is matched by the company so the company puts in 10%*3,090 = 309

Total amount deposited = 3,090 + 309 = 3,399

This amount will increase by 3% every year (as salary increases by 3% annually)

Future value (FV) of a growing annuity = P/(r-g)*[(1+r)^n - (1+g)^n] where P = 3,090; r = 2% (fixed rate of the fund); g = 3%; n = 30

FV = 3,399/(2% - 3%)*[(1+2%)^30 - (1+3%)^30] = 209,344.71

The fund already had 25,000 at the beginning so its FV will be 25,000*(1+2%)^30 = 45,284.04

Total amount in the fund at the time of retirement = 209,344.71 + 45,284.04 = 254,628.75

Note: This is calculated based on the assumption that the deposits are made at the end of the year, as the question does not specify when deposits are made. If deposits are made at the beginning of the year, then calculations will change according to annuity due formula.