A man invested a sum of money at compound interest. It amounted to ₹12100 in two years and to ₹13310 in three years. The rate of interest per annum is:

Formula for compound interest = $$P(1+\frac{R}{100})^T - P$$

Amount = compound interest + P = $$P(1+\frac{R}{100})^T$$

Where P = principal amount, R = rate of interest, T = time.

$$12100=P(1+\frac{R}{100})^2$$    Eq.(i)

$$13310=P(1+\frac{R}{100})^3$$    Eq.(ii)

$$\frac{Eq.(ii)}{Eq.(i)}\ =\ \frac{13310}{12100}\ =\ \frac{P(1+\frac{R}{100})^3}{P(1+\frac{R}{100})^2}$$

$$\frac{11}{10}\ =\ (1+\frac{R}{100})$$

$$\frac{11}{10}-1=\frac{R}{100}$$

$$\frac{1}{10}=\frac{R}{100}$$

rate of interest per annum = R = 10%