If the difference between the compound and simple interest on a certain sum of money for 2 years at 8% per annum is 3160, find the sum.

Options

A. 4,93,750
B. 3,37,500
C. 4,63,500
D. 4,39,500

Answer

To solve the problem, we need to find the principal sum based on the difference between compound interest (CI) and simple interest (SI) over 2 years at an interest rate of 8% per annum.

### Step-by-Step Solution:

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

2. **Identify Given Values**:
From the problem, we have:
- Difference = 3160
- Rate (R) = 8%
- Time = 2 years

3. **Substitute the Values into the Formula**:
Plugging the values into the formula gives:
\[ 3160 = P \times \frac{8^2}{100^2} \]

4. **Calculate \( \frac{8^2}{100^2} \)**:
Calculate \( 8^2 \) and \( 100^2 \):
\[ 8^2 = 64 \quad \text{and} \quad 100^2 = 10000 \]
Therefore:
\[ \frac{8^2}{100^2} = \frac{64}{10000} = 0.0064 \]

5. **Rearranging the Equation**:
Now, substitute this back into the equation:
\[ 3160 = P \times 0.0064 \]

6. **Solve for Principal (P)**:
To find \( P \), rearrange the equation:
\[ P = \frac{3160}{0.0064} \]

7. **Perform the Division**:
Calculate the value:
\[ P = 3160 \div 0.0064 = 493750 \]

8. **Final Answer**:
Thus, the principal sum is:
\[ P = 493750 \]

### Conclusion:
The sum of money (the principal) is **493750**.