The difference between simple interest and compound interest on ₹ 2500 at 4% per annum for two years is (in ₹):

Options

A. ₹40
B. ₹4
C. ₹45
D. ₹14

Answer

To find the difference between simple interest (SI) and compound interest (CI) on ₹2500 at an interest rate of 4% per annum for 2 years, we can 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 (₹2500)
- \(R\) = Rate of interest (4%)
- \(T\) = Time (2 years)

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

### 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 \(1 + \frac{4}{100} = 1.04\):
\[ CI = 2500 \times (1.04)^2 - 2500 \]
Calculating \((1.04)^2\):
\[ (1.04)^2 = 1.0816 \]
Now substituting back:
\[ CI = 2500 \times 1.0816 - 2500 \]
Calculating:
\[ CI = 2704 - 2500 = ₹204 \]

### Step 3: Find the Difference between CI and SI
Now, we find the difference:
\[ Difference = CI - SI = 204 - 200 = ₹4 \]

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

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