What will be the difference between the simple interest and compound interest of Rs 4400 for 2 years at `5%` per annum?

Options

A. Rs 55
B. Rs 507
C. Rs 403
D. Rs 11

Answer

To find the difference between the simple interest (SI) and compound interest (CI) on Rs 4400 for 2 years at a rate of 5% 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:
- \( P = 4400 \) (Principal amount)
- \( R = 5 \) (Rate of interest)
- \( T = 2 \) (Time in years)

Substituting the values:
\[ SI = \frac{4400 \times 5 \times 2}{100} \]
Calculating this gives:
\[ SI = \frac{44000}{100} = 440 \text{ rupees} \]

### Step 2: Calculate Compound Interest (CI)
The formula for Compound Interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]
Where \( A \) is the amount after time \( T \).

Substituting the values:
\[ A = 4400 \left(1 + \frac{5}{100}\right)^2 \]
This simplifies to:
\[ A = 4400 \left(1 + 0.05\right)^2 = 4400 \left(1.05\right)^2 \]
Calculating \( (1.05)^2 \):
\[ (1.05)^2 = 1.1025 \]
Now substituting back:
\[ A = 4400 \times 1.1025 = 4851 \text{ rupees} \]

To find the Compound Interest (CI), we subtract the principal from the amount:
\[ CI = A - P = 4851 - 4400 = 451 \text{ rupees} \]

### Step 3: Calculate the Difference between CI and SI
Now we find the difference:
\[ \text{Difference} = CI - SI = 451 - 440 = 11 \text{ rupees} \]

### Final Answer:
The difference between the simple interest and compound interest is **11 rupees**.

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