since a year has 12 months, then 3 years will be 36 months, now, 3 years and 9 months is just 36 + 9 = 45 months. So we can say that 3 years and 9 months is really 45/12 of a year.
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$800\\ r=rate\to 2.65\%\to \frac{2.65}{100}\dotfill &0.0265\\ t=years\to \frac{45}{12}\dotfill &\frac{15}{4} \end{cases} \\\\\\ A=800[1+(0.0265)(\frac{15}{4})]\implies A=800(1+0.099375) \\\\\\ A=800(1.099375)\implies A=879.5[/tex]
