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Compound Interest — MATHS STD 8 — Question

Gujarat BoardEnglish MediumSTD 8MATHSCompound Interest5 Marks
Question
Kamala borrowed from Ratan a certain sum at a certain rate for two years simple interest. She lent this sum at the same rate to Hari for two years compound interest. At the end of two years she received $Rs. 210$ as compound interest, but paid Rs. 200 only as simple interest. Find the sum and the rate of interest.
✓

Answer

Let the sum be $Rs. P$ and the rate of interest be $R\%$.
We know that Kamla paid $Rs. 200$ as simple interest.
$\therefore\ 200=\frac{\text{PR(2)}}{100}$ $\text{PR}=10,000...(1)$
Also, Kamla received $Rs. 210$ as compound interest.
$\therefore\ 210=\text{P}\Big(1+\frac{\text{R}}{100}\Big)^{2}-1$
$210(10,000)=\text{P}(\text{R}^{2}+200\text{R})$
$210\text{ R}=\text{ R}^{2}+200\text{R}$ [from $(1)$]
$R = 10\% p.a$.
Putting the equation in $(1)$,
we get: $P = 1,000$
Thus, the required sum is $Rs. 1,000$ and the rate of interest is $10\%$.

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