The difference between compound interest and simple interest on Rs. 2500 for 2 years at 4% per annum is

Answer

To find the difference between compound interest (CI) and simple interest (SI) on Rs. 2500 for 2 years at an interest rate of 4% per annum, we will follow these steps:

### Step 1: Calculate Simple Interest (SI)
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount (Rs. 2500)
- \( R \) = Rate of interest (4%)
- \( T \) = Time (2 years)

Substituting the values:
\[ SI = \frac{2500 \times 4 \times 2}{100} \]
\[ SI = \frac{20000}{100} = 200 \]

### Step 2: Calculate Compound Interest (CI)
The formula for Compound Interest is:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
Substituting the values:
\[ CI = 2500 \left(1 + \frac{4}{100}\right)^2 - 2500 \]
Calculating \( \left(1 + \frac{4}{100}\right) \):
\[ 1 + \frac{4}{100} = 1.04 \]
Now, calculating \( (1.04)^2 \):
\[ (1.04)^2 = 1.0816 \]
Now substituting back:
\[ CI = 2500 \times 1.0816 - 2500 \]
\[ CI = 2704 - 2500 = 204 \]

### Step 3: Calculate the Difference between CI and SI
Now, we find the difference:
\[ \text{Difference} = CI - SI \]
\[ \text{Difference} = 204 - 200 = 4 \]

### Final Answer
The difference between compound interest and simple interest on Rs. 2500 for 2 years at 4% per annum is Rs. 4.

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