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Question

At what rate percent per annum will a sum of Rs. 2000 amount to Rs. 2205 in 2 years at compound interest?


A
3%
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B
2%
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C
5%
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D
4%
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Solution

The correct option is A $$5$$%
Given that, a sum of $$Rs.\ 2000$$ amounts to $$Rs.\ 2205$$ in $$2$$ years.
To find out: The rate of interest

For compound interest, we know that,
$$A=P\left(1+\dfrac{R}{100}\right)^T$$

Here, $$P=Rs.\ 2000,\ A=Rs.\ 2205$$ and $$T=2\,$$years.

$$\therefore \ 2205=2000\times \left(1+\dfrac{R}{100}\right)^2$$

$$\Rightarrow$$  $$\dfrac{441}{400}=\left(1+\dfrac{R}{100}\right)^2$$

$$\Rightarrow$$  $$\dfrac{21}{20}=\left(1+\dfrac{R}{100}\right)$$

$$\Rightarrow$$  $$R=\dfrac{1}{20}\times 100=5\%$$

Hence, the required rate of interest is $$5\%$$.

Mathematics

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