What is the difference the compound interest and simple interest on ₹ 2500 for 2 years at 4% p.a.

Answer

To solve the problem of finding the difference between compound interest and simple interest on ₹2500 for 2 years at 4% per annum, we will follow these steps:

### Step 1: Calculate Simple Interest (SI)

The formula for Simple Interest is given by:

\[ \text{SI} = \frac{P \times R \times N}{100} \]

Where:
- \( P = 2500 \) (Principal)
- \( R = 4 \) (Rate of interest per annum)
- \( N = 2 \) (Time in years)

Substituting the values:

\[ \text{SI} = \frac{2500 \times 4 \times 2}{100} \]

Calculating the numerator:

\[ 2500 \times 4 = 10000 \]
\[ 10000 \times 2 = 20000 \]

Now divide by 100:

\[ \text{SI} = \frac{20000}{100} = 200 \]

### Step 2: Calculate Compound Interest (CI)

The formula for Compound Interest is given by:

\[ A = P \left(1 + \frac{R}{100}\right)^N \]

Where \( A \) is the total amount after time \( N \).

Substituting the values:

\[ A = 2500 \left(1 + \frac{4}{100}\right)^2 \]

Calculating \( \left(1 + \frac{4}{100}\right) \):

\[ 1 + \frac{4}{100} = 1 + 0.04 = 1.04 \]

Now, raise this to the power of 2:

\[ A = 2500 \times (1.04)^2 \]

Calculating \( (1.04)^2 \):

\[ (1.04)^2 = 1.0816 \]

Now, calculate \( A \):

\[ A = 2500 \times 1.0816 = 2704 \]

Now, the Compound Interest (CI) can be calculated as:

\[ \text{CI} = A - P = 2704 - 2500 = 204 \]

### Step 3: Find the Difference between CI and SI

Now, we find the difference between Compound Interest and Simple Interest:

\[ \text{Difference} = \text{CI} - \text{SI} = 204 - 200 = 4 \]

### Final Answer

The difference between the compound interest and simple interest on ₹2500 for 2 years at 4% p.a. is **₹4**.

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