Question

You just graduated from college and your new employer offers a 401(k) where they match your contribution, dollar for dollar. You want to know the accumulated balance in your 401(k), including your employer's contribution, assuming you contribute either $950 per month or $1,150 per month, and the fund earns 8.1% annually. Assuming you and your employer each invest $950 per month, what will be the value of your 401(k) at the end of 24 years?​ Use Future Value Formula.

Answer 1

The accumulated balance in the 401(k), considering your and your employer's monthly contributions of $950 each, with an 8.1% annual interest rate after 24 years, is approximately $1,056,614.13.

To find the accumulated balance in your 401(k) at the end of 24 years, including your employer's contribution, you can use the future value formula:

`\[ FV = P * ((1 + r)^(nt) - 1)/(r) \]`

Where:

- P is the monthly contribution (your and your employer's combined contribution),

- r is the monthly interest rate (annual interest rate divided by 12),

- n is the number of times the interest is compounded per year (12 for monthly),

- t is the number of years.

Given P = $950 + $950 = $1900 , r = 0.081/12 , n = 12 , and t = 24 , plug these values into the formula:

`\[ FV = 1900 * ((1 + 0.081/12)^(12 * 24) - 1)/(0.081/12) \]`

Calculating this expression, the final result for the accumulated balance in your 401(k) after 24 years is approximately $1,056,614.13.