keeping in mind that 3 months is not even a year, but since there are 12 months in a year, 3 months is really 3/12 years, therefore,
[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill&100\\ P=\textit{original amount deposited}\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\to \frac{3}{12}\dotfill &\frac{1}{4} \end{cases} \\\\\\ 100=P\left( 0.04\cdot \frac{1}{4} \right)\implies 100=P(0.01)\implies \cfrac{100}{0.01}=P\implies 10000=P[/tex]
