The difference between the compound interest and simple interest on a sum of ₹2,500 for 2 years is ₹100. Find the rare of interest per annum, if the nominal rate of interest per annum is the same for both simple and compound interest, and in the case of compound interest, the interest is compounded annually.

20%

The formula used here is,

Difference in the simple interest and compound interest on a certain sum at R% per annum in 2 years = (CI - SI) = $\frac{PR^2}{100^2}$

⇒ Difference in the simple interest and compound interest on Rs.2500 at R% per annum in 2 years = Rs. 100

⇒ 100 = $\frac{2500 ×R^2}{100^2}$

⇒  100  = \(\frac{R²}{4}\)

⇒  R = 20%

Thus, the rate is 20%