The difference between the interest compounded annually and the simple interest on a sum of ₹$31,250$ for $2$ years at $8\%$ per annum is:

The formula for the difference between compound interest ($CI$) and simple interest ($SI$) for $2$ years is given by:
$$CI-SI=P{\left(\frac{R}{100}\right)}^2$$

Where:
* $P=\text{₹}31,250$
* $R=8\%$

Substitute the values into the formula:
$$CI-SI=31250\times {\left(\frac{8}{100}\right)}^2$$
$$CI-SI=31250\times {\left(\frac{2}{25}\right)}^2$$
$$CI-SI=31250\times \frac{4}{625}$$

Dividing $31250$ by $625$:
$$31250÷625=50$$
$$CI-SI=50\times 4=\text{₹}200$$