The difference between the compound interest and the simple inter… - Vidyadip

Question

The difference between the compound interest and the simple interest on a certain sum for 3 years at 10% per annum is Rs. 93. Find the sum.

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Answer

$\therefore$ Simple interest (S.I) $=\frac{\text{prt}}{100}$
$=\frac{100\times10\times3}{100}=\text{Rs. }30$
Amount (A) $=\text{P}\Big(1+\frac{\text{r}}{100}\Big)^{\text{n}}$
$=\text{Rs. }100\Big(1+\frac{10}{100}\Big)^3$
$=\text{Rs. }100\times\Big(\frac{11}{10}\Big)^3$
$=\text{Rs. }100\times\frac{11}{10}\times\frac{11}{10}\times\frac{11}{10}$
$=\text{Rs. }\frac{1331}{10}$
$\therefore$ C.I = A - P $=\text{Rs. }\frac{1331}{10}-\text{Rs. }100$
$=\text{Rs. }\frac{331}{10}$
Difference between C.I and S.I
$=\text{Rs. }\frac{1331}{10}-\text{Rs. }30=\text{Rs. }\frac{31}{10}$
If difference is $=\text{Rs. }\frac{31}{10},$ then sum
and if difference is Rs. 93 then sum
$=\text{Rs. }\frac{100\times93\times10}{31}$
$=\text{Rs. }3000$

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