Mr. Vinod borrowed Rs. 9000 at 5% annum compound interest. The compound interest compounded annually for 2 years is :

Options

A. 922.5
B. 9921.5
C. 921.5
D. 9922.5

Answer

To find the compound interest for Mr. Vinod who borrowed Rs. 9000 at a rate of 5% per annum for 2 years, we can follow these steps:

### Step 1: Identify the formula for compound interest
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:
- \( P = 9000 \)
- \( R = 5 \)
- \( T = 2 \)

Substituting these values into the formula:
\[ CI = 9000 \left(1 + \frac{5}{100}\right)^2 - 9000 \]

### Step 3: Simplify the expression inside the parentheses
Calculate \( 1 + \frac{5}{100} \):
\[ 1 + \frac{5}{100} = 1 + 0.05 = 1.05 \]

### Step 4: Raise the result to the power of T
Now, raise \( 1.05 \) to the power of 2:
\[ (1.05)^2 = 1.1025 \]

### Step 5: Multiply by the principal and subtract the principal
Now substitute back into the CI formula:
\[ CI = 9000 \times 1.1025 - 9000 \]
Calculating \( 9000 \times 1.1025 \):
\[ 9000 \times 1.1025 = 9912.5 \]
Now subtract the principal:
\[ CI = 9912.5 - 9000 = 912.5 \]

### Step 6: Finalize the answer
Thus, the compound interest for 2 years is:
\[ CI = 912.5 \]

### Summary
The compound interest compounded annually for 2 years is Rs. 912.5.