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

Options

A. A) `Rs. 10000 `
B. B) `Rs. 20000`
C. C) `Rs. 5000 `
D. D) `Rs. 15000`

Answer

To solve the problem, we need to find the principal amount (sum of money) 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 Simple Interest (SI)**:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
where \( P \) is the principal, \( R \) is the rate of interest, and \( T \) is the time in years.

2. **Calculate Simple Interest for 2 Years**:
Given \( R = 4\% \) and \( T = 2 \) years:
\[ \text{SI} = \frac{P \times 4 \times 2}{100} = \frac{8P}{100} = 0.08P \]

3. **Understand the Formula for Compound Interest (CI)**:
The formula for CI after 2 years is:
\[ \text{CI} = P \left(1 + \frac{R}{100}\right)^T - P \]
For \( R = 4\% \) and \( T = 2 \):
\[ \text{CI} = P \left(1 + \frac{4}{100}\right)^2 - P = P \left(1.04^2\right) - P \]
Calculating \( 1.04^2 \):
\[ 1.04^2 = 1.0816 \]
Therefore,
\[ \text{CI} = P(1.0816) - P = 0.0816P \]

4. **Find the Difference Between CI and SI**:
The difference between CI and SI is given as Rs. 8:
\[ \text{CI} - \text{SI} = 0.0816P - 0.08P = 0.0016P \]
Setting this equal to 8:
\[ 0.0016P = 8 \]

5. **Solve for Principal (P)**:
To find \( P \):
\[ P = \frac{8}{0.0016} \]
Calculating \( P \):
\[ P = 5000 \]

### Conclusion:
The principal amount (sum of money) is Rs. 5000.