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Find the rate percent per annum if Rs. 2000 amount to Rs. 2662 in 1 1/2 years, interest being compounded half-yearly?

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Best answer

Given, 

Principal = Rs.2000 

Amount = Rs.2662

Time \(={1}\frac{1}{2}\) years \(=\frac{3}{2}\times2\) = 3 half years

Let rate = R% per annum, \(\frac{R}{2}\text%\) half yearly

So,

A = \({P}[({1}+\frac{R}{100})^T]\)

\(={2000}[({1}+\frac{R}{2\times100})^3]\) = 2662

\(=({1}+\frac{R}{100})^3\) \(=\frac{2662}{2000}\) \(=\frac{1331}{1000}\) \(=(\frac{11}{10})^3\)

\(={1}+\frac{R}{200}\) \(=\frac{11}{10}\)

\(=\frac{R}{200}\) \(=\frac{11}{10}-{1}\) \(=\frac{1}{10}\)

= R \(=\frac{1\times200}{10}\) = 20% per annum

Hence , 

Rate = 20% per annum

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