Given,
Principal = Rs. 4400
Amount = Rs.4576
Rate = 8% p.a \(=\frac{8}{2} ={4}\text%\) half yearly
Let time = T years = 2T half years
So,
A \(={P}[({1}+\frac{4}{100})^T]\)
\(={4400}[({1}+\frac{4}{100})^{2T}]\) = 4576
\(=(\frac{26}{25})^{2T}\) \(=\frac{4576}{4400}\) \(=\frac{26}{25}\)
= 2T = 1
\(={T}=\frac{1}{2}\) years
Hence,
Time \(=\frac{1}{2}\) years