Question

Find the simple interest on $Rs.4000$ at $7.5\%p.a.$ for $3$ years $3$ months. Also, find the amount.

Answer 1

Step 1: Calculate the simple interest for the given data.

Simple interest can be calculated using the formula,

$\mathit{S}\mathbf{.}\mathit{I}\mathbf{.}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{P}\mathbf{\times }\mathbf{R}\mathbf{\times }\mathbf{T}}{\mathbf{100}}$

Where, $S.I.$ is the simple interest, $P$ is the principal, $R$ is the rate of interest in percentage and $T$ is the time period

Thus,

$$\begin{gathered} T=\frac{3\times 12+3}{12} \\ T=\frac{{\displaystyle \stackrel{13}{\cancel{39}}}}{{\displaystyle \underset{4}{\cancel{12}}}} \\ T=\frac{13}{4} \end{gathered}$$

$\begin{array}{rcl}S.I.& =& \frac{{\displaystyle \stackrel{10}{\cancel{40}}}\cancel{00}\times 7.5\times \left({\displaystyle \raisebox{1ex}{$13$}\!\left/ \!\raisebox{-1ex}{$\cancel{4}$}\right.}\right)}{\cancel{100}}\\ & =& Rs.975\end{array}$

Step 2: Calculate the amount corresponding to the principal and simple interest.

Total amount can be calculated using the formula,

$A=P+S.I.$

Where, $A$ is the amount

Thus,

$\begin{array}{rcl}A& =& 4000+975\\ & & \\ & =& Rs.4975\end{array}$

Hence, the required simple interest is $Rs.975$ and the amount is $Rs.4975$.