since a year has 12 months, after 21 months that'd be 21/12 of a year.
[tex]~~~~~~ \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}\dotfill &\$500\\ 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\to \frac{21}{12}\dotfill &\frac{7}{4} \end{cases}[/tex]
[tex]A=500\left(1+\frac{0.06}{4}\right)^{4\cdot \frac{7}{4}}\implies A=500(1.015)^7\implies A\approx 554.92[/tex]
