Mr. Arun borrowed Rs. 6500 at 4% per annum compound interest. The compound interest compounded annually for 2 years is:

Options

A. Rs. 530.4
B. Rs. 7300.4
C. Rs. 503.4
D. Rs. 7030.4

Answer

To find the compound interest for Mr. Arun's loan, we will use the formula for compound interest:

**Compound Interest (CI) = P * (1 + r/100)^t - P**

Where:
- P = Principal amount (initial amount borrowed)
- r = Rate of interest per annum
- t = Time in years

### Step 1: Identify the values
- Principal (P) = Rs. 6500
- Rate (r) = 4%
- Time (t) = 2 years

### Step 2: Substitute the values into the formula
Using the formula, we substitute the values:
\[ CI = 6500 * \left(1 + \frac{4}{100}\right)^2 - 6500 \]

### Step 3: Simplify the expression inside the parentheses
Calculate \(1 + \frac{4}{100}\):
\[ 1 + \frac{4}{100} = 1 + 0.04 = 1.04 \]

### Step 4: Raise the result to the power of 2
Now we need to calculate \((1.04)^2\):
\[ (1.04)^2 = 1.04 * 1.04 = 1.0816 \]

### Step 5: Multiply by the principal
Now we multiply this result by the principal:
\[ 6500 * 1.0816 = 7020.4 \]

### Step 6: Subtract the principal from this amount
Now, we find the compound interest by subtracting the principal from this amount:
\[ CI = 7020.4 - 6500 = 520.4 \]

### Final Answer
The compound interest compounded annually for 2 years is **Rs. 520.4**.

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