Question 10: Salma invested Rs. \(350000\) in a bank, which paid simple profit at the rate of \(7\frac{1}{4}\%\) per annum. After 2 years, the rate was increased to \(8\%\) per annum. Find the amount she had at the end of \(7\) years.
Solution:
Let
\[
\begin{align*}
\text{Principal}=p&\small{=350000}\\
\text{Rate for first 2 years} =R_1&=7\frac{1}{4}\%\\
&=\frac{29}{4}\%\\
\text{Rate for 5 years} =R_2&= 8\%\\
\end{align*}
\]
Profit for first two years
\[
\begin{align*}
P_1&=\frac{principal \times Time \times Rate}{100}\\
&=\frac{350000\times 2\times \frac{29}{4}}{100}\\
&=\frac{350000\times 2\times 29}{100\times 4}\\
&=50750\text{ RS}\\
\end{align*}
\]
Profit for remaining five years
\[
\begin{align*}
P_{2} &=\frac{350000\times 5\times 8}{100}\\
&=140000\text{ RS}
\end{align*}
\]
Total Amount after 7 years
\[
\begin{align*}
\text{Total} &=\ p+P_{1} +P_{2}\\
&=350000+50750+140000\\
&=540750\text{ RS}\\
\end{align*}
\]