Find the difference between the simple interest and the compound interest on Rs. 15000 at 12% per annum for 2 years (in Rs. ).

Options

A. 216
B. 240
C. 180
D. 192

Explanation

To find the difference between the simple interest (SI) and compound interest (CI) on Rs. 15,000 at 12% per annum for 2 years, we will follow these steps:

### Step 1: Calculate Simple Interest (SI)
The formula for Simple Interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P = 15000 \) (Principal amount)
- \( R = 12 \) (Rate of interest)
- \( T = 2 \) (Time in years)

Substituting the values:
\[ \text{SI} = \frac{15000 \times 12 \times 2}{100} \]
\[ \text{SI} = \frac{360000}{100} \]
\[ \text{SI} = 3600 \]

### Step 2: Calculate Compound Interest (CI)
The formula for Compound Interest is:
\[ \text{CI} = P \left(1 + \frac{R}{100}\right)^T - P \]
Substituting the values:
\[ \text{CI} = 15000 \left(1 + \frac{12}{100}\right)^2 - 15000 \]
\[ \text{CI} = 15000 \left(1 + 0.12\right)^2 - 15000 \]
\[ \text{CI} = 15000 \left(1.12\right)^2 - 15000 \]
\[ \text{CI} = 15000 \times 1.2544 - 15000 \]
\[ \text{CI} = 18816 - 15000 \]
\[ \text{CI} = 3816 \]

### Step 3: Find the Difference between CI and SI
Now, we find the difference:
\[ \text{Difference} = \text{CI} - \text{SI} \]
\[ \text{Difference} = 3816 - 3600 \]
\[ \text{Difference} = 216 \]

### Final Answer
The difference between the compound interest and simple interest on Rs. 15,000 at 12% per annum for 2 years is **Rs. 216**.

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