Question

Between the ages of 22 and 37, you deposit $300 per month into a 401K and your employer matches your contributions dollar for dollar. The interest rate is 6% compounded monthly. 1.) What is the value of your 401K after 15 years? 2.) Suppose you resign from your position after 15 years with the company, but your money remains in the account and continues to earn interest at the same rate. With no further deposits, how much will be in the account when you retire at age 67? 3.) What is the difference between the amount of money in the 401K and the amount you contributed? Include commas, a dollar sign, and round to cents.

Answer 1

Future value of annuity is calculated as C*(((1+r)^n)-1)/r; where C is the periodic cashflow, r is the discount rate and n is the number of periods.

Given that employer matches dollar to dollar. So, monthly amount is 300+300= $600. interest rate per month is 6%/12= 0.5%.

1).

Value after 15 years= 600*((1+0.5%)^180)-1)/0.5%= $174491.23

2).

After 30 years, with no further deposits, Value will be 174491.23*(1+0.5%)^(30*12)= $1050886.54

3).

The amount we contributed= (300*180)= $54000

Difference between the amount of money in the 401K and the amount you contributed= 1050886.54-54000= $996886.54