Determine the principal amount that at the rate of $5\%$ compound interest per annum earns a compound interest of $\text{Rs. }615$ after two years.

Let the principal amount be $P$.
The formula for compound interest ($CI$) after $n$ years at a rate of $R\%$ per annum is given by:

$$CI=P\left[{\left(1+\frac{R}{100}\right)}^n-1\right]$$

Given parameters:

* Compound Interest ($CI$) = $\text{Rs. }615$
* Rate of interest ($R$) = $5\%$
* Time period ($n$) = $2\text{ years}$

Substituting these values into the formula:

$$615=P\left[{\left(1+\frac{5}{100}\right)}^2-1\right]$$

$$615=P\left[{\left(\frac{21}{20}\right)}^2-1\right]$$

$$615=P\left[\frac{441}{400}-1\right]$$

$$615=P\left[\frac{41}{400}\right]$$

Solving for $P$:

$$P=\frac{615\times 400}{41}$$

$$P=15\times 400=\text{Rs. }6000$$

Thus, the principal amount is $\text{Rs. }6000$.