The difference between the compound interest and the simple interest on a certain sum of money at 4% per annum for 2 years is Rs. 1.40. Find the sum.

Answer

To find the sum of money (principal) based on the given difference between compound interest (CI) and simple interest (SI) over 2 years at an interest rate of 4% per annum, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for the Difference**:
The difference between the compound interest and simple interest for 2 years can be calculated using the formula:
\[ \text{Difference} = P \times \left(\frac{R}{100}\right)^2 \]
where \( P \) is the principal amount and \( R \) is the rate of interest.

2. **Identify the Given Values**:
- Difference = Rs. 1.40
- Rate \( R = 4\% \)

3. **Substitute the Values into the Formula**:
\[ 1.40 = P \times \left(\frac{4}{100}\right)^2 \]

4. **Calculate the Square of the Rate**:
\[ \left(\frac{4}{100}\right)^2 = \frac{16}{10000} \]

5. **Rewrite the Equation**:
Substitute the squared rate back into the equation:
\[ 1.40 = P \times \frac{16}{10000} \]

6. **Multiply Both Sides by 10000**:
\[ 1.40 \times 10000 = 16P \]
\[ 14000 = 16P \]

7. **Solve for \( P \)**:
\[ P = \frac{14000}{16} \]

8. **Calculate the Value of \( P \)**:
\[ P = 875 \]

### Final Answer:
The sum (principal) is Rs. 875.

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