What will be the difference between the simple inerest and compound interest accrued on an amount of Rs. 12000 at the end of 3 years @ 10 p.a. ?

Options

A. Rs. 276
B. Rs. 372
C. Rs. 272
D. Rs. 324

Answer

To find the difference between the simple interest (SI) and compound interest (CI) accrued on an amount of Rs. 12,000 at the end of 3 years at a rate of 10% 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. 12,000
- \( R = \) Rate of interest = 10%
- \( T = \) Time (in years) = 3 years

Substituting the values:
\[ SI = \frac{12000 \times 10 \times 3}{100} = \frac{1200000}{100} = 12000 \]

### 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:
\[ CI = 12000 \left(1 + \frac{10}{100}\right)^3 - 12000 \]
\[ CI = 12000 \left(1 + 0.1\right)^3 - 12000 \]
\[ CI = 12000 \left(1.1\right)^3 - 12000 \]
Calculating \( (1.1)^3 \):
\[ (1.1)^3 = 1.331 \]
Now substituting back:
\[ CI = 12000 \times 1.331 - 12000 \]
\[ CI = 15972 - 12000 = 3972 \]

### Step 3: Calculate the Difference between CI and SI
Now, we find the difference between Compound Interest and Simple Interest:
\[ \text{Difference} = CI - SI \]
\[ \text{Difference} = 3972 - 12000 \]
\[ \text{Difference} = 3972 - 12000 = 2972 \]

### Final Answer
The difference between the simple interest and compound interest accrued on the amount of Rs. 12,000 at the end of 3 years at a rate of 10% per annum is Rs. 2972.

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