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 = ?

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Principal  =  Rs 8000 \\ Amount   =  Rs 8820 \\ Let Rate  = R \\ Time  =  2 years \\ By using formula, \\ \Rightarrow 8820 = 8000 {(1 + \frac{R}{100})}^{2} \\ \Rightarrow \frac{8820}{8000} = {(1 + \frac{R}{100})}^{2} \\ \Rightarrow \frac{441}{400} = {(1 + \frac{R}{100})}^{2} \\ Taking square root of both sides, \\ \Rightarrow \frac{21}{20} = (1 + \frac{R}{100}) \\ \Rightarrow R = 5 % \end{aligned}

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