The sum of the simple interest and the compound interest on ₹5,600 at the same rate of interest per annum for two years is ₹2,061.36, when in the case of compound interest, it is compounded annually. What is the rate of interest per annum?

The sum of the simple interest and the compound interest on ₹5,600 at the same rate of interest per annum for two years is ₹2,061.36, when in the case of compound interest, it is compounded annually.

Sum of SI and CI = $$\frac{principal\times\ rate\times\ time}{100}+principal\left(1+\frac{rate}{100}\right)^{time}\ -\ principal$$

$$2061.36=\frac{5600\times\ rate\times\ 2}{100}+5600\left(1+\frac{rate}{100}\right)^2\ -\ 5600$$

$$2061.36=5600\left[\frac{rate\times\ 2}{100}+\left(1+\frac{rate}{100}\right)^2\ -\ 1\right]$$

$$\frac{2061.36}{5600}=\left[\frac{2\times\ rate}{100}+1+\frac{2\times\ rate}{100}+\frac{rate^2}{10000}\ -\ 1\right]$$

$$\frac{206136}{560000}=\left[\frac{4\times\ rate}{100}+\frac{rate^2}{10000}\ \right]$$

$$\frac{3681}{100}=\left[4\times\ rate+\frac{rate^2}{100}\ \right]$$    Eq.(i)

$$\frac{3681}{100}=\left[4\times\ 9+\frac{9^2}{100}\ \right]$$

$$\frac{3681}{100}=\left[36+\frac{81}{100}\ \right]$$

$$\frac{3681}{100}=\frac{3681}{100}$$