A sum of money invested at compound interest amounts to ₹ $1,600$ in $3$ years and ₹ $2,000$ in $4$ years. Find the rate of interest per annum.

In compound interest, the amount at the end of a year becomes the principal for the next year.
Amount after $3\text{years}(A_3)=₹1,600$
Amount after $4\text{years}(A_4)=₹2,000$

The interest earned in the $4^{\text{th}}$ year is on the amount $A_3$.

$$\text{Interest}=A_4-A_3=2000-1600=₹400$$

$$\text{Rate of Interest}(R)=\left(\frac{\text{Interest for the year}}{\text{Principal for that year}}\right)\times 100$$

$$R=\left(\frac{400}{1600}\right)\times 100$$

$$R=\frac{1}{4}\times 100=25\%$$