Find the differnece between simple interest and compound interest on rupes 4,000 and for two years at 10 % per annum .

Answer

To find the difference between simple interest and compound interest on ₹4,000 for two years at a rate of 10% per annum, 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 (₹4,000)
- \( R \) = Rate of interest (10%)
- \( T \) = Time period in years (2 years)

Substituting the values:

\[ SI = \frac{4000 \times 10 \times 2}{100} \]

Calculating:

\[ SI = \frac{80000}{100} = 800 \]

So, the Simple Interest for 2 years is **₹800**.

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

The formula for Compound Interest is:

\[ CI = A - P \]

Where \( A \) is the amount after time \( T \), calculated using the formula:

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

Substituting the values:

\[ A = 4000 \left(1 + \frac{10}{100}\right)^2 \]

This simplifies to:

\[ A = 4000 \left(1 + 0.1\right)^2 = 4000 \left(1.1\right)^2 \]

Calculating \( (1.1)^2 \):

\[ (1.1)^2 = 1.21 \]

Now substituting back:

\[ A = 4000 \times 1.21 = 4840 \]

Now, we can calculate the Compound Interest:

\[ CI = A - P = 4840 - 4000 = 840 \]

So, the Compound Interest for 2 years is **₹840**.

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

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

\[ \text{Difference} = CI - SI = 840 - 800 \]

Calculating:

\[ \text{Difference} = 40 \]

Thus, the difference between Compound Interest and Simple Interest is **₹40**.

### Final Answer:
The difference between the compound interest and simple interest is **₹40**.

---