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The compound interest on a certain sum in 2 frac 1...

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Compound Interest
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The compound interest on a certain sum in $$2\frac{1}{2}$$ years at 10% p.a., interest compounded yearly, is Rs. 1,623. The sum is:

Answer & Solution
Correct Answer: Option B
$$\eqalign{ & 2{\text{ year}} \to {\text{CI}} \cr & = 10 + 10 + \frac{{10 \times 10}}{{100}} = 21\% \cr & {\text{In 2}}\frac{1}{2}{\text{ year CI}} \cr & = 21 + 5 + \frac{{21 \times 5}}{{100}} = 27.05\% \cr & P \times \frac{{27.05}}{{100}} = 1623 \cr & P = {\text{Rs}}{\text{. 6000}} \cr} $$
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