The difference between the simple and compound Interest on a certain sum of money at 5% rate of interest per annum for 2 years is 15. Then the sum is :

Options

A. `Rs. 6,500`
B. `Rs. 5,500`
C. `Rs. 6,000`
D. `Rs. 7,000 `

Answer

To solve the problem, we need to find the principal amount (P) based on the difference between simple interest (SI) and compound interest (CI) over 2 years at a rate of 5% per annum, which is given as 15.

### Step-by-Step Solution:

1. **Understand the Formula for the Difference Between SI and CI**:
The difference between the simple interest and compound interest for 2 years can be calculated using the formula:
\[ \text{Difference} = \frac{P \times R^2}{100^2} \]
where \( P \) is the principal amount, \( R \) is the rate of interest, and the difference is given as 15.

2. **Substitute the Known Values**:
We know that:
- The difference = 15
- The rate \( R = 5\% \)

Plugging these values into the formula, we get:
\[ 15 = \frac{P \times 5^2}{100^2} \]

3. **Calculate \( 5^2 \) and \( 100^2 \)**:
\[ 5^2 = 25 \]
\[ 100^2 = 10000 \]

4. **Rewrite the Equation**:
Now substituting these values back into the equation:
\[ 15 = \frac{P \times 25}{10000} \]

5. **Multiply Both Sides by 10000**:
\[ 15 \times 10000 = P \times 25 \]
\[ 150000 = P \times 25 \]

6. **Solve for \( P \)**:
Now, divide both sides by 25:
\[ P = \frac{150000}{25} \]
\[ P = 6000 \]

Thus, the principal amount is **6000**.