The sum of money that yields a compound interest of Rs. 420 during the second year at 5% per annum is

Answer

To find the sum of money (principal) that yields a compound interest of Rs. 420 during the second year at a rate of 5% per annum, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We know that the compound interest for the second year is Rs. 420 and the interest rate is 5% per annum. We need to find the principal amount (P).

2. **Calculate the Interest for the Second Year**: The interest for the second year is calculated based on the principal and the interest from the first year. The interest for the first year is 5% of the principal (P).

\[ \text{Interest for the first year} = \frac{5}{100} \times P = 0.05P \]

3. **Calculate the Principal for the Second Year**: The principal for the second year becomes the original principal plus the interest from the first year.

\[ \text{Principal for the second year} = P + 0.05P = 1.05P \]

4. **Calculate the Interest for the Second Year**: The interest for the second year is then calculated as 5% of the new principal.

\[ \text{Interest for the second year} = \frac{5}{100} \times (1.05P) = 0.0525P \]

5. **Set Up the Equation**: We know that the interest for the second year is Rs. 420. Therefore, we can set up the equation:

\[ 0.0525P = 420 \]

6. **Solve for P**: To find P, we rearrange the equation:

\[ P = \frac{420}{0.0525} \]

Now, calculating this gives:

\[ P = \frac{420 \times 10000}{525} = \frac{4200000}{525} = 8000 \]

7. **Conclusion**: The principal amount (sum of money) that yields a compound interest of Rs. 420 during the second year at 5% per annum is Rs. 8000.