Mt. Anin 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 solve the problem of calculating the compound interest for Mr. Anil who borrowed Rs. 6500 at 4% per annum for 2 years, we will follow these steps:

### Step 1: Understand the Compound Interest Formula
The formula for calculating compound interest (CI) is:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
where:
- \(P\) = Principal amount (initial amount borrowed)
- \(R\) = Rate of interest per annum
- \(T\) = Time in years

### Step 2: Substitute the Values into the Formula
Given:
- \(P = 6500\)
- \(R = 4\%\)
- \(T = 2\)

Substituting these values into the formula:
\[ CI = 6500 \left(1 + \frac{4}{100}\right)^2 - 6500 \]

### Step 3: Simplify the Expression Inside the Parentheses
Calculate \(1 + \frac{4}{100}\):
\[ 1 + \frac{4}{100} = 1 + 0.04 = 1.04 \]

### Step 4: Calculate \(1.04^2\)
Now, we need to calculate \(1.04^2\):
\[ 1.04^2 = 1.04 \times 1.04 = 1.0816 \]

### Step 5: Substitute Back and Calculate CI
Now substitute \(1.04^2\) back into the compound interest formula:
\[ CI = 6500 \times 1.0816 - 6500 \]
Calculating \(6500 \times 1.0816\):
\[ 6500 \times 1.0816 = 7030.4 \]
Now, subtract the principal:
\[ CI = 7030.4 - 6500 = 530.4 \]

### Final Answer
The compound interest for 2 years is:
\[ \text{CI} = 530.4 \]