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in Compound Interest by (28.9k points)
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At what rate percent will a sum of Rs. 1000 amount to Rs. 1102.50 in 2 years at compound interest?

1 Answer

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Best answer

Given, 

Principal = Rs.1000 

Amount = Rs.1102.50 

Time = 2 years 

Let rate of interest = R % per annum 

So,

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

\(={1000}({1}+\frac{R}{100})^2\) = 1102.50

\(=({1}+\frac{R}{100})^2\) \(=\frac{1102.50}{1000}\) \(=\frac{4410}{4000}\) \(=(\frac{21}{20})^2\)

\(=1+\frac{R}{100}\) \(=\frac{21}{20}\)

\(=\frac{R}{100}\) \(=\frac{21}{20}-1\) \(=\frac{1}{20}\)

= R \(=\frac{1}{20}\times100\) = 5%

Hence, 

Rate of interest = 5 % per annum

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