Answer
A) $\$14163.246$.
B) $\$1663.246$
Work Step by Step
(a)
To find the total savings, we will have to calculate annuity,
$A=\frac{P\left[ {{\left( 1+\frac{r}{n} \right)}^{nt}}-1 \right]}{\left( \frac{r}{n} \right)}$
Here $P=\$2500$ and $r=0.0625$ for $t=5\,\text{years}$. Compounded annually, hence $n=1$.
Thus
$\begin{align}
& A=\frac{2500\left[ {{\left( 1+\frac{0.0625}{1} \right)}^{5}}-1 \right]}{\left( \frac{0.0625}{1} \right)} \\
& =\frac{2500\left[ {{\left( 1.0625 \right)}^{5}}-1 \right]}{\left( 0.0625 \right)} \\
& =\frac{2500\left[ \left( 1.3540 \right)-1 \right]}{\left( 0.0625 \right)} \\
& =14163.246
\end{align}$
(b)
Here $P=\$2500$ and $r=0.0625$ for $t=5\,\text{years}$. Compounded annually, hence $n=1$.
Thus
$\begin{align}
& A=\frac{2500\left[ {{\left( 1+\frac{0.0625}{1} \right)}^{5}}-1 \right]}{\left( \frac{0.0625}{1} \right)} \\
& =\frac{2500\left[ {{\left( 1.0625 \right)}^{5}}-1 \right]}{\left( 0.0625 \right)} \\
& =\frac{2500\left[ \left( 1.3540 \right)-1 \right]}{\left( 0.0625 \right)} \\
& =14163.246
\end{align}$
Now, interest is the difference between annuity and total deposit and total deposit is given by: $P\times n\times t$.
So:
$\begin{align}
& Interest=14163.246-2500\times 1\times 5 \\
& =14163.246-12500 \\
& =1663.246
\end{align}$
