Difference of the compound interest received in first year and second year at 20% per annum at CI is Rs 1200 then find the sum?

Options

A. A)Rs 25,000
B. B)Rs 36,000
C. C)Rs 35,000
D. D)Rs. 30,000

Answer

To solve the problem of finding the principal amount given the difference in compound interest for the first and second year, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Rate of Interest**:
The rate of interest is given as 20% per annum.

2. **Understand the Concept of Compound Interest**:
The compound interest for the first year is calculated on the principal amount. For the second year, the interest is calculated on the new amount, which is the principal plus the interest from the first year.

3. **Let the Principal Amount be P**:
We will denote the principal amount as P.

4. **Calculate the Compound Interest for the First Year**:
The interest for the first year (CI1) can be calculated as:
\[ CI1 = P \times \frac{20}{100} = 0.2P \]

5. **Calculate the Amount at the End of the First Year**:
The total amount at the end of the first year (A1) is:
\[ A1 = P + CI1 = P + 0.2P = 1.2P \]

6. **Calculate the Compound Interest for the Second Year**:
The interest for the second year (CI2) is calculated on the amount at the end of the first year:
\[ CI2 = A1 \times \frac{20}{100} = 1.2P \times 0.2 = 0.24P \]

7. **Find the Difference in Compound Interest**:
The difference between the compound interest received in the second year and the first year is:
\[ \text{Difference} = CI2 - CI1 = 0.24P - 0.2P = 0.04P \]

8. **Set Up the Equation**:
According to the problem, this difference is given as Rs 1200:
\[ 0.04P = 1200 \]

9. **Solve for P**:
To find the principal amount (P), we rearrange the equation:
\[ P = \frac{1200}{0.04} = 1200 \times 25 = 30000 \]

10. **Conclusion**:
The principal amount (P) is Rs 30,000.

### Final Answer:
The sum (principal amount) is Rs 30,000.