On a certain sum of money, the simple interest for 2 years is Rs. 200 at the rate of 7% per annum. Find the difference in CI and SI.

Answer

To solve the problem of finding the difference between Compound Interest (CI) and Simple Interest (SI) for a certain sum of money, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Simple Interest (SI) for 2 years = Rs. 200
- Rate of interest (R) = 7% per annum
- Time (T) = 2 years

2. **Calculate the Principal (P):**
- The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
- Rearranging the formula to find the Principal (P):
\[ P = \frac{SI \times 100}{R \times T} \]
- Substituting the values:
\[ P = \frac{200 \times 100}{7 \times 2} = \frac{20000}{14} = 1428.57 \text{ (approximately)} \]

3. **Calculate the Simple Interest for 2 Years:**
- We already know that the Simple Interest for 2 years is Rs. 200.

4. **Calculate the Compound Interest (CI) for 2 Years:**
- The formula for Compound Interest is:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
- Substituting the values:
\[ CI = 1428.57 \left(1 + \frac{7}{100}\right)^2 - 1428.57 \]
- Calculating \( \left(1 + \frac{7}{100}\right)^2 \):
\[ = 1428.57 \left(1.07\right)^2 = 1428.57 \times 1.1449 \approx 1630.61 \]
- Now, calculating CI:
\[ CI = 1630.61 - 1428.57 \approx 202.04 \]

5. **Find the Difference between CI and SI:**
- The difference between Compound Interest and Simple Interest is:
\[ \text{Difference} = CI - SI = 202.04 - 200 = 2.04 \]

### Final Answer:
The difference between Compound Interest and Simple Interest for the given sum of money is approximately Rs. 2.04.

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