a)
[tex]\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad
\begin{cases}
A=\textit{compounded amount}\\
P=\textit{original amount deposited}\to &\$1500\\
r=rate\to7\%\to \frac{7}{100}\to &0.07\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{semi-annually, thus twice}
\end{array}\to &2\\
t=years\to &5
\end{cases}
\\\\\\
A=1500\left(1+\frac{0.07}{2}\right)^{2\cdot 5}[/tex]
b)
[tex]\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad
\begin{cases}
A=\textit{compounded amount}\\
P=\textit{original amount deposited}\to &\$1500\\
r=rate\to7\%\to \frac{7}{100}\to &0.07\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{quarterly, 4 quarters, thus}
\end{array}\to &4\\
t=years\to &5
\end{cases}
\\\\\\
A=1500\left(1+\frac{0.07}{4}\right)^{4\cdot 5}[/tex]
c)
[tex]\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad
\begin{cases}
A=\textit{compounded amount}\\
P=\textit{original amount deposited}\to &\$1500\\
r=rate\to7\%\to \frac{7}{100}\to &0.07\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{monthly, 12 months, thus}
\end{array}\to &12\\
t=years\to &5
\end{cases}
\\\\\\
A=1500\left(1+\frac{0.07}{12}\right)^{12\cdot 5}[/tex]
d)
[tex]\bf \qquad \textit{Compound Interest Earned Amount}
\\\\
A=Pe^{rt}
\quad
\begin{cases}
A=\textit{compounded amount}\\
P=\textit{original amount deposited}\to &\$1500\\
r=rate\to7\%\to \frac{7}{100}\to &0.07\\
t=years\to &5
\end{cases}
\\\\\\
A=1500e^{0.07\cdot 5}[/tex]
