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