[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 &\$3000\\
r=rate\to 5.2\%\to \frac{5.2}{100}\to &0.052\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{quarterly, thus four}
\end{array}\to &4\\
t=years\to &10
\end{cases}
\\\\\\
A=3000\left(1+\frac{0.052}{4}\right)^{4\cdot 10}\implies A=3000(1.013)^{40}
\\\\\\
A\approx 5029.201878874637[/tex]
