A sum becomes $\text{Rs. }13,520$ in $2$ years at $4\%$ per annum compound interest. Then the original sum is:

The formula for the total accumulated amount under compound interest is:
$$A=P{\left(1+\frac{R}{100}\right)}^t$$

Given:

* Amount ($A$) $=\text{Rs. }13,520$
* Rate ($R$) $=4\%$ p.a.
* Time ($t$) $=2$ years

Substitute the values into the equation:

$$13520=P{\left(1+\frac{4}{100}\right)}^2$$

$$13520=P{\left(1+\frac{1}{25}\right)}^2$$

$$13520=P{\left(\frac{26}{25}\right)}^2$$

$$13520=P\times \frac{676}{625}$$

$$P=\frac{13520\times 625}{676}$$

Since $676\times 20=13520$:

$$P=20\times 625=12500$$

Thus, the original sum is $\text{Rs. }12,500$.