Question

A. suppose that between the ages of 22 and 26, you contribute $1000 per year to a 401k and your employer contributes $500 per year on your behalf. the interest rate is 9.4% compounded annually. what is the value of the 401k after 4 years?

B. Supoose that after 4 years of working for this firm, you move on to a new job. However, you keep your accumulated retirement funds in the 401k. How much money will you have in the plan when you reach age 65?
C. What is the difference between the amount of money you will have accumulated in the 401k and the amount you contributed to the plan?

Answer 1

The value of the 401k after 4 years is $6810.73. When you reach age 65, you will have $74,246.97 in the 401k. The difference between the amount accumulated in the 401k and the amount contributed to the plan is $811.73.

Step-by-step explanation:

In order to calculate the value of the 401k after 4 years, we need to calculate the future value of the contributions and the employer contributions. Here's how:

1. The future value of your contributions: $1000 per year for 4 years, with an annual interest rate of 9.4%, compounded annually. Using the formula for compound interest, the future value of your contributions will be $1000*(1+0.094)^4 = $4540.49.
2. The future value of the employer contributions: $500 per year for 4 years, with an annual interest rate of 9.4%, compounded annually. Using the same formula, the future value of the employer contributions will be $500*(1+0.094)^4 = $2270.24.
3. Finally, to find the total value of the 401k, we add the future value of the contributions and the future value of the employer contributions: $4540.49 + $2270.24 = $6810.73.

Therefore, the value of the 401k after 4 years is $6810.73.

Now, let's move on to part B of the question.

To calculate the amount of money in the 401k when you reach age 65, we need to calculate the future value of the contributions and the employer contributions over the remaining years until age 65. Here's how:

1. The number of remaining years is 65 - 26 = 39 years.
2. Using the same formula for compound interest, the future value of your contributions over the remaining years will be $1000*(1+0.094)^39 = $49,497.98.
3. The future value of the employer contributions over the remaining years will be $500*(1+0.094)^39 = $24,748.99.
4. To find the total value of the 401k at age 65, we add the future value of the contributions and the future value of the employer contributions: $49,497.98 + $24,748.99 = $74,246.97.

Therefore, you will have $74,246.97 in the 401k when you reach age 65.

Finally, let's move on to part C of the question.

The difference between the amount of money you will have accumulated in the 401k and the amount you contributed to the plan can be found by subtracting the total contributions from the total value of the 401k. In this case, the total contributions are $1000 per year for 4 years + $500 per year for 4 years = $6000. And the total value of the 401k is $6810.73. Therefore, the difference is $6810.73 - $6000 = $811.73.

So, the difference between the amount accumulated in the 401k and the amount contributed to the plan is $811.73.