A sum of Rs. 8000 will amount to Rs. 8820 in 2 years if the interest is calculated every year. The rate of compound interest is = ?

$$\eqalign{ & {\text{Principal = Rs 8000}} \cr & {\text{Amount = Rs 8820}} \cr & {\text{Let Rate = }}R \cr & {\text{Time = 2 years}} \cr & {\text{By using formula, }} \cr & \Rightarrow 8820 = 8000{\left( {1 + \frac{R}{{100}}} \right)^2} \cr & \Rightarrow \frac{{8820}}{{8000}} = {\left( {1 + \frac{R}{{100}}} \right)^2} \cr & \Rightarrow \frac{{441}}{{400}} = {\left( {1 + \frac{R}{{100}}} \right)^2} \cr & {\text{Taking square root of both sides,}} \cr & \Rightarrow \frac{{21}}{{20}} = \left( {1 + \frac{R}{{100}}} \right) \cr & \Rightarrow R = 5\% \cr} $$