[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill &\$15000\\ P=\textit{original amount deposited}\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &4 \end{cases}[/tex]
[tex]15000=P\left(1+\frac{0.06}{4}\right)^{4\cdot 4}\implies 15000=P(1.015)^{16} \\\\\\ \cfrac{15000}{1.015^{16}}=P\implies 11820.47\approx P[/tex]
