well, since a year has 12 months, 3 months are just 1/4 of a year, so let's use that.
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$4000\\ r=rate\to 5.25\%\to \frac{5.25}{100}\dotfill &0.0525\\ t=years\to \frac{3}{12}\dotfill &\frac{1}{4} \end{cases} \\\\\\ A=4000[1+(0.0525)(\frac{1}{4})]\implies A=4000\left( \frac{1621}{1600} \right)\implies \boxed{A=4052.5} \\\\\\ \stackrel{interest~paid}{4052.5~~ - ~~4000\implies \boxed{52.5}}[/tex]
