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%
B
2%
C
5%
D
4%

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 interestFor 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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