If the difference between CI and SI on a certain sum at 4% per annum for 2 years is Rs. 25, find the sum.

Options

A. Rs. 18625
B. Rs. 16625
C. Rs. 14625
D. Rs. 15625

Answer

To solve the problem of finding the principal sum when the difference between Compound Interest (CI) and Simple Interest (SI) for 2 years at a rate of 4% per annum is Rs. 25, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formulas**:
- The formula for Simple Interest (SI) for 2 years is:
\[ SI = \frac{P \times R \times T}{100} \]
- The formula for Compound Interest (CI) for 2 years is:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]

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

3. **Calculate CI for 2 Years**:
- Using the formula for CI:
\[ CI = P \left(1 + \frac{4}{100}\right)^2 - P \]
- Simplifying:
\[ CI = P \left(1.04^2\right) - P = P(1.0816) - P = 0.0816P \]

4. **Find the Difference Between CI and SI**:
- The difference is given as:
\[ CI - SI = 0.0816P - 0.08P = 0.0016P \]
- We know this difference equals Rs. 25:
\[ 0.0016P = 25 \]

5. **Solve for Principal (P)**:
- Rearranging the equation:
\[ P = \frac{25}{0.0016} \]
- Calculating \( P \):
\[ P = 25 \div 0.0016 = 15625 \]

### Final Answer:
The principal sum is Rs. 15,625.

---