Question
The difference between the compound interest and simple interest on a certain sum for $2$ years at $7.5\%$ per annum is $Rs. 360.$ Find the sum.
✓
Answer
Let the sum be $P.$ Thus, we have: $\text{CI}-\text{SI}=360$
$\Big[\text{P}\Big(1+\frac{\text{R}}{100}\Big)^{\text{n}}-\text{P}\Big]-\frac{\text{P}\times7.5\times2}{100}=360$
$\text{P}\Big[\Big(1+\frac{7.5}{100}\Big)^{2}-1\Big]-\frac{\text{p}\times7.5\times2}{100}=360$
$\text{P}[1.155625-1]-0.15\text{ P}$
$=3600.155625\text{ P}-0.15\text{ P}$
$=3600.005625\text{ P}=360\text{ P}$
$=\frac{360}{0.005625}\text{ P}=64000$
Thus, the required sum is $Rs. 64.$
$\Big[\text{P}\Big(1+\frac{\text{R}}{100}\Big)^{\text{n}}-\text{P}\Big]-\frac{\text{P}\times7.5\times2}{100}=360$
$\text{P}\Big[\Big(1+\frac{7.5}{100}\Big)^{2}-1\Big]-\frac{\text{p}\times7.5\times2}{100}=360$
$\text{P}[1.155625-1]-0.15\text{ P}$
$=3600.155625\text{ P}-0.15\text{ P}$
$=3600.005625\text{ P}=360\text{ P}$
$=\frac{360}{0.005625}\text{ P}=64000$
Thus, the required sum is $Rs. 64.$
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