Find the difference between the compound interest and the simple interest for the sum Rs. 625 at 8% per annum for 2 years.

Answer

To find the difference between the compound interest (CI) and simple interest (SI) for a sum of Rs. 625 at an interest rate of 8% per annum over 2 years, we can use a specific formula that simplifies the calculation.

### Step-by-Step Solution:

1. **Identify the Variables:**
- Principal (P) = Rs. 625
- Rate of Interest (R) = 8% per annum
- Time (T) = 2 years

2. **Use the Formula for the Difference:**
The difference between compound interest and simple interest for 2 years can be calculated using the formula:
\[ \text{Difference} = P \times \frac{R}{100} \times \frac{R}{100} \]
This simplifies to:
\[ \text{Difference} = P \times \frac{R^2}{10000} \]

3. **Substitute the Values:**
Substitute P = 625 and R = 8 into the formula:
\[ \text{Difference} = 625 \times \frac{8^2}{10000} \]

4. **Calculate \(8^2\):**
\[ 8^2 = 64 \]

5. **Substitute Back:**
\[ \text{Difference} = 625 \times \frac{64}{10000} \]

6. **Simplify the Calculation:**
- First, calculate \(625 \times 64\):
\[ 625 \times 64 = 40000 \]
- Now divide by 10000:
\[ \text{Difference} = \frac{40000}{10000} = 4 \]

7. **Final Answer:**
The difference between the compound interest and simple interest is Rs. 4.