The simple interest and compound interest on a certain sum for $2$ years is INR $1250$ and INR $1475$, respectively. The rate of interest per annum (compounded annually) in percentage is:

Time period $= 2$ years

Simple Interest (SI) $=$ INR $1250$

Compound Interest (CI) $=$ INR $1475$

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The difference between CI and SI:

$1475 - 1250 = 225$

This difference represents interest earned on the first year's interest for one year.

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For Simple Interest:

$SI = \dfrac{P \times R \times T}{100}$

$1250 = \dfrac{P \times R \times 2}{100}$

$P \times R = 62500$ ... (Equation 1)

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For 2 years, the difference between CI and SI:

$225 = P \times \left(\dfrac{R}{100}\right)^2$

$225 = P \times \dfrac{R^2}{10000}$

$P \times R^2 = 2250000$ ... (Equation 2)

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From Equation 2 divided by Equation 1:

$\dfrac{P \times R^2}{P \times R} = \dfrac{2250000}{62500}$

$R = 36$

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Therefore, the rate of interest per annum is $36\%$.