What would be the compound interest obtained on an amount of Rs. 8850 at the rate of 12 p.c.p.a. after two years.

Options

A. Rs. 2625.44
B. Rs. 2450.44
C. Rs. 2384.24
D. Rs. 2251.44

Answer

To find the compound interest on an amount of Rs. 8850 at a rate of 12% per annum after 2 years, we can follow these steps:

### Step 1: Identify the formula for compound interest
The formula for calculating the amount \( A \) after \( T \) years with principal \( P \), rate \( R \), and time \( T \) is given by:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]

### Step 2: Substitute the values into the formula
Here, we have:
- Principal \( P = 8850 \)
- Rate \( R = 12 \)
- Time \( T = 2 \)

Substituting these values into the formula:
\[ A = 8850 \left(1 + \frac{12}{100}\right)^2 \]

### Step 3: Simplify the expression inside the parentheses
Calculate \( 1 + \frac{12}{100} \):
\[ 1 + \frac{12}{100} = 1 + 0.12 = 1.12 \]

### Step 4: Raise the result to the power of 2
Now we calculate:
\[ A = 8850 \times (1.12)^2 \]
Calculating \( (1.12)^2 \):
\[ (1.12)^2 = 1.2544 \]

### Step 5: Multiply by the principal
Now, multiply this result by the principal:
\[ A = 8850 \times 1.2544 \]
Calculating this gives:
\[ A = 11011.44 \]

### Step 6: Calculate the compound interest
The compound interest \( CI \) is given by:
\[ CI = A - P \]
Substituting the values:
\[ CI = 11011.44 - 8850 \]
Calculating this gives:
\[ CI = 2161.44 \]

### Final Answer
The compound interest obtained on an amount of Rs. 8850 at the rate of 12% per annum after two years is Rs. 2161.44.

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