[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to &\$37644\\
r=rate\to 12\%\to \frac{12}{100}\to &0.12\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{semiannually, thus twice}
\end{array}\to &2\\
t=years\to &4
\end{cases}
\\\\\\
A=37644\left(1+\frac{0.12}{2}\right)^{2\cdot 4}\implies A=37644(1.06)^8[/tex]
