The difference between simple and compound interests on a sum of money at 4% per annum for 2 years is Rs. 8. The sum is

Options

A. Rs. 400
B. Rs. 800
C. Rs. 4,000
D. Rs. 5,000

Answer

To solve the problem, we need to find the principal amount based on the difference between simple interest (SI) and compound interest (CI) over 2 years at an interest rate of 4% per annum.

### Step-by-Step Solution:

1. **Understand the Formula for the Difference Between CI and SI:**
The difference between compound interest and simple interest for 2 years can be expressed as:
\[ \text{Difference} = \text{CI} - \text{SI} = P \times \frac{R^2}{100^2} \]
where \( P \) is the principal amount, and \( R \) is the rate of interest.

2. **Substituting the Known Values:**
From the problem, we know:
- The difference is Rs. 8
- The rate \( R = 4\% \)
- The time period is 2 years.

Plugging these values into the formula gives:
\[ 8 = P \times \frac{4^2}{100^2} \]

3. **Calculating \( R^2 \) and \( 100^2 \):**
Calculate \( 4^2 \) and \( 100^2 \):
\[ 4^2 = 16 \quad \text{and} \quad 100^2 = 10000 \]

Therefore, we can rewrite the equation as:
\[ 8 = P \times \frac{16}{10000} \]

4. **Rearranging the Equation to Solve for \( P \):**
To isolate \( P \), we can rearrange the equation:
\[ P = 8 \times \frac{10000}{16} \]

5. **Calculating \( P \):**
Now, calculate \( P \):
\[ P = 8 \times 625 = 5000 \]

6. **Conclusion:**
The principal amount is Rs. 5000.

### Final Answer:
The sum is Rs. 5000.

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