Answer
See below:
Work Step by Step
(a)
Compute the value of 401(k) after the end of 18 years using the equation as shown below:
\[\begin{align}
& A=\frac{P\left[ {{\left( 1+r \right)}^{t}}-1 \right]}{r} \\
& =\frac{\$4500\left[{{\left(1+0.083\right)}^{18}}-1\right]}{0.083}\\&=\frac{\$4500\left[{{\left(1.083\right)}^{18}}-1\right]}{0.083}\\&=\$173,527\end{align}\]
(b)
Compute the value of the investment at the age of 65 years using the equation as shown below:
\[\begin{align}
& A=P{{\left( 1+r \right)}^{t}} \\
& =\$173,527{{\left(1+0.083\right)}^{25}}\\&=\$1,273,733\end{align}\]
(c)
Compute the difference between the amount of money accumulated in 401(k) and the amount contributed to the plan using the equation as shown below:
\[\begin{align}
& \text{Difference between amount accumulated and contributed}=\text{Amount accumulated at the age of 65} \\
& -\text{Amount deposited in 18 years} \\
& =\$1,273,733-\left(18\times\$3000\right)\\&=\$1,273,733-\$54,000\\&=\$1,219,733\end{align}\]
