Given,
Time = 2 years = 2×2 = 4 half years
Let rate = R % per annum \(=\frac{R}{2}\text%\) half yearly
Let principal = P
Amount becomes = 4P
So,
\(A ={P}[({1}+\frac{R}{100})^T]\)
\(={P}[({1}+\frac{R}{2\times100})^4\) = 4P
\(={1}+\frac{R}{200}\) \(={4}^{\frac{1}{4}}\)= 1.4142
\(=\frac{R}{200} = 1.4142-1\) = 0.4142
= R = \({0.4142\times200}\) = 82.84%
Hence ,
Rate = 82.84 %