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Compound Interest — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSCompound Interest5 Marks
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.
✓

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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