The simple interest and compound interest of a certain sum of money for two years are $\text{Rs. }400$ and $\text{Rs. }410$ respectively. Then the rate of interest per annum is:

We know that simple interest is calculated uniformly every year on the principal amount.
* Total $\text{SI}$ for $2$ years = $\text{Rs. }400$
* $\text{SI}$ for the $1\text{st}$ year = $\frac{400}{2}=\text{Rs. }200$
* $\text{SI}$ for the $2\text{nd}$ year = $\text{Rs. }200$

For the first year, compound interest ($\text{CI}$) and simple interest ($\text{SI}$) are exactly identical.

The total compound interest for $2$ years is given as $\text{Rs. }410$.
The difference between $\text{CI}$ and $\text{SI}$ for $2$ years is:

$$\text{Difference}=\text{CI}-\text{SI}=410-400=\text{Rs. }10$$

This difference of $\text{Rs. }10$ is the interest earned on the first year's interest ($\text{Rs. }200$) during the second year.

Therefore, the rate of interest ($R$) can be determined as:

$$R=\frac{\text{Difference}}{\text{SI for 1st year}}\times 100$$

$$R=\frac{10}{200}\times 100=5\%$$

Thus, the rate of interest per annum is $5\%$.