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Rachna borrowed a certain sum at the rate of 15% per annum. If she paid at the end of two years Rs. 1290 as interest compounded annually, find the sum she borrowed.

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Best answer

Given, 

Rate = 15% p.a 

Time = 2 years 

C.I = Rs. 1290 

Let principal = P 

So, 

Compound interest \(={P}[({1}+\frac{R}{100})^T-{1}]\)

\(={P}[({1}+\frac{15}{100})^2-{1}]\) = 1290

\(={P}[(\frac{23}{20})^2-{1}]\) = 1290

\(={P}\times\frac{129}{400}\) = 1290

\(={P}=\frac{1290\times400}{129}\) = Rs. 4000

Hence, 

Principal = Rs. 4000

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