a. Suppose that between the ages of 22 and 36 , you contribute $$ 2000$ per year to a $401 (k)$ and your employer contributes $$ 1000$ per year on your behalf. The interest rate is $7.6 %$ compounded annually. What is the value of the $401 (k)$ after 14 years? b. Suppose that after 14 years of working for this firm, you move on to a new job. However, you keep your accumulated retirement funds in the $401 (k)$ . 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 $401 (k)$ and the amount you contributed to the plan?
(i) Click the icon to view some finance formulas.
a. The value of the $401 (k)$ after 14 years is $$ 70599$ .
(Do not round until the final answer. Then round to the nearest dollar as needed.)
b. The money accumulated in the plan when reaching age 65 is $$ ◻$
(Do not round until the final answer. Then round to the nearest dollar is needed.)
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$The value of the 401(k) after 14 years is approximately $70599.$

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Step 1 ：Define the variables: the payment amount per period $P = $ 3000$ , the interest rate per period $r = 0.076$ , the number of compounding periods per year $n = 1$ , and the time the money is invested for in years $t = 14$ .

Step 2 ：Calculate the future value using the formula $F V = P \times ((1 + r)^{n \times t} - 1) / r$ .

Step 3 ：The calculated future value of the 401(k) after 14 years is approximately $70599.

Step 4 ： $The value of the 401(k) after 14 years is approximately $70599.$

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