The difference between the compound interest and the simple interest at the same rate of interest, for the amount $\text{Rs. }5,000$ in $2$ years, is $\text{Rs. }32$. The rate of interest is:

The standard formula for the difference ($D$) between Compound Interest ($CI$) and Simple Interest ($SI$) for a period of $2$ years is:
$$D=P{\left(\frac{R}{100}\right)}^2$$

Given:

* Difference ($D$) = $\text{Rs. }32$
* Principal ($P$) = $\text{Rs. }5,000$

Substitute the values into the formula:

$$32=5000\times \frac{R^2}{10000}$$

$$32=\frac{5000}{10000}\times R^2$$

$$32=\frac{1}{2}\times R^2$$

$$R^2=32\times 2=64$$

$$R=\sqrt{64}=8\%$$