A sum of money is invested at compound interest, which is compounded annually. The sum grows to ₹1000 after three years, and ₹1100 after four years. What is the rate of interest per annum?

The sum grows to ₹1000 after three years, and ₹1100 after four years.

As per the formula of compound interest, two equations are formed which are given below. 

Here P = principal amount and R = rate of interest.

$$P(1+\frac{R}{100})^{3} = 1000$$    Eq.(i)
$$P(1+\frac{R}{100})^{4} = 1100$$    Eq.(ii)

Now Eq.(i) is divided by Eq.(ii) to obtain the value of 'R'.

$$\frac{Eq.(i)}{Eq.(ii)} = \frac{P(1+\frac{R}{100})^{3}}{P(1+\frac{R}{100})^{4}} = \frac{1000}{1100}$$

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

$$\frac{100}{100+R} = \frac{10}{11}$$

100+R = 110

R = 10%