[tex] \bf ~~~~~~ \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad
\begin{cases}
A=\textit{accumulated amount}\to &\$5000\\
P=\textit{original amount deposited}\\
r=rate\to 3\%\to \frac{3}{100}\to &0.03\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{quarterly, thus four}
\end{array}\to &4\\
t=years\to &4
\end{cases} [/tex]
[tex] \bf 5000=P\left(1+\frac{0.03}{4}\right)^{4\cdot 4}\implies \cfrac{5000}{\left(1+\frac{0.03}{4}\right)^{4\cdot 4}}=P\implies \cfrac{5000}{(1.0075)^{16}}=P
\\\\\\
4436.58827712\approx P [/tex]
