a. Suppose that between the ages of 22 and 36 , you contribute $\$ 2000$ per year to a $401(\mathrm{k})$ and your employer contributes $\$ 1000$ per year on your behalf. The interest rate is $7.6 \%$ compounded annually. What is the value of the $401(\mathrm{k})$ 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 $401(\mathrm{k})$. How much money will you have in the plan when you reach age 65 ? $\mathrm{c}$. What is the difference between the amount of money you will have accumulated in the $401(\mathrm{k})$ and the amount you contributed to the plan?
(i) Click the icon to view some finance formulas.
a. The value of the $401(\mathrm{k})$ 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 $\$ \square$
(Do not round until the final answer. Then round to the nearest dollar is needed.)
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Answer
\(\boxed{\text{The value of the 401(k) after 14 years is approximately \$70599.}}\)
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 \(FV = P \times ((1 + r)^{n \times t} - 1) / r\).
Step 3 ：The calculated future value of the 401(k) after 14 years is approximately \$70599.
Step 4 ：\(\boxed{\text{The value of the 401(k) after 14 years is approximately \$70599.}}\)
