Answer
A) $\$171271$.
B) $\$135271$.
Work Step by Step
(a)
In the given case $P=\$50$ and $r=0.065$ for $t=40\,\text{years}$. It is compounded monthly, hence $n=12$.
Thus:
$\begin{align}
& A=\frac{75\left[ {{\left( 1+\frac{0.065}{12} \right)}^{12\times 40}}-1 \right]}{\left( \frac{0.065}{12} \right)} \\
& =\frac{75\left[ {{\left( 1.0054 \right)}^{12\times 40}}-1 \right]}{\left( 0.0054 \right)} \\
& =\frac{75\left[ \left( 13.3696 \right)-1 \right]}{\left( 0.0054 \right)} \\
& =171271
\end{align}$
Hence, the total savings after $65\ years$ is $\$171271$.
