Identify the given compound interests for the first and second years.

Let $CI_1$ be the compound interest for the first year.
Let $CI_2$ be the compound interest for the second year.
We are given:
$CI_1 = \text{Rs. } 20$
$CI_2 = \text{Rs. } 23$

The compound interest for the first year is calculated on the principal amount.
The compound interest for the second year is calculated on the amount accumulated at the end of the first year (Principal + $CI_1$).
The difference between $CI_2$ and $CI_1$ represents the interest earned on the interest of the first year.

The additional interest earned in the second year compared to the first year is:

This Rs. 3 is the interest earned on $CI_1$ (Rs. 20) for one year.

We can consider $CI_1$ as the principal for calculating this additional interest.
Let $P' = CI_1 = \text{Rs. } 20$.
Let $I' = \text{Additional Interest} = \text{Rs. } 3$.
Time $T = 1$ year.
The formula for simple interest is $I = \frac{P \times R \times T}{100}$.
Substituting the values:

Multiply both sides by 5:

The rate of interest is 15% per annum.

The final answer is $15\% \text{ P.C.P.A.}$.