You're on a roll — Q. The Compound interest of certain for first and Second year is Rs. 20 and Rs. 23 respectively. Find the rate of interest in P.C.P.A. Step 1: 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: $CI_1 = \text{Rs. } 20$ $CI_2 = \text{Rs. } 23$ Step 2: Understand the relationship between compound interest for consecutive years. 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. Step 3: Calculate the interest earned on the first year's interest. The additional interest earned in the second year compared to the first year is: $$ \text{Additional Interest} = CI_2 - CI_1 = 23 - 20 = \text{Rs. } 3 $$ This Rs. 3 is the interest earned on $CI_1$ (Rs. 20) for one year. Step 4: Use the simple interest formula to find the rate of interest. 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: $$ 3 = \frac{20 \times R \times 1}{100} $$ Step 5: Solve for the rate of interest ($R$). $$ 3 = \frac{20R}{100} $$ $$ 3 = \frac{R}{5} $$ Multiply both sides by 5: $$ R = 3 \times 5 $$ $$ R = 15 $$ The rate of interest is 15% per annum. The final answer is $\boxed{15\% \text{ P.C.P.A.}}$. Send me the next one 📸