bearing in mind that a year has 4 quarters, so 15 quarters is really 15/4 years.
[tex] \bf ~~~~~~ \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad
\begin{cases}
A=\textit{accumulated amount}\to &\$24000\\
P=\textit{original amount deposited}\\
r=rate\to 8\%\to \frac{8}{100}\to &0.08\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{quarterly, thus four}
\end{array}\to &4\\
t=years\to &\frac{15}{4}
\end{cases} [/tex]
[tex] \bf 24000=P\left(1+\frac{0.08}{4}\right)^{4\cdot \frac{15}{4}}\implies 24000=P(1.02)^{15}
\\\\\\
\cfrac{24000}{1.02^{15}}=P\implies 17832.35\approx P [/tex]
