401k Math problem

Question

Part 1. Suppose that between the ages of 23-45 you contribute 3000 per year to a 401k and your employer contributes 1500 per year on your behalf. The interest rate is 8.1% compounded annually. What is the value of the 401k, rounded to the nearest dollar, after 22 years.
Part 2. Suppose that after 22 years of working at this firm you move to a new job. However you will keep your accumulated retirement funds in the 401k. How much money, to the nearest dollar, will you have in the plan when you reach age 65?

Answer 1

 

The compounding interest formula with annual contributions is:

P(1 + r)^Y + c[ ((1 + r)^Y - 1) / r ]

 

Where P is the starting principal amount which in this problem is 4500,

 r is 8.1% = 0.081

Y is the number of years which is 22

and C is the annual contributions which is the same as P= 4500

 

4500(1.081)^22 + 4500[ ((1.081)^22-1)/0.081]

 

4500(5.548368111) + 4500[(5.548368111-1)/0.081]

 

4500((5.548368111) + 4500(68.498372)

 

24967.6565 +308242.674

 

333210.33

 

 

Part B is simply the compound interest formula, as annual contributions stop.

 

 333210.33 (1.081)^20 = 1582091.19