What would be the compound interest drawn on an amount of Rs. 18,400 @ 12 per cent p.a. at the end of 3 years ?

Options

A. Rs. `4680cdot96`
B. Rs. `7450cdot6752`
C. Rs.`6235cdot2143`
D. Rs.`8042cdot16`

Answer

To find the compound interest on an amount of Rs. 18,400 at a rate of 12% per annum at the end of 3 years, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 18,400
- Rate of interest (R) = 12% per annum
- Time (T) = 3 years

### Step 2: Use the formula for compound interest
The formula for calculating the amount (A) after time T with compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]

### Step 3: Substitute the values into the formula
Substituting the values into the formula:
\[ A = 18400 \left(1 + \frac{12}{100}\right)^3 \]

### Step 4: Simplify the expression
First, calculate \(1 + \frac{12}{100}\):
\[ 1 + \frac{12}{100} = 1 + 0.12 = 1.12 \]

Now substitute this back into the equation:
\[ A = 18400 \times (1.12)^3 \]

### Step 5: Calculate \( (1.12)^3 \)
Now calculate \( (1.12)^3 \):
\[ (1.12)^3 = 1.404928 \] (approximately)

### Step 6: Calculate the amount (A)
Now substitute \( (1.12)^3 \) back into the equation for A:
\[ A = 18400 \times 1.404928 \]
\[ A \approx 25813.07 \] (approximately)

### Step 7: Calculate the compound interest (CI)
Now, we can find the compound interest (CI) using the formula:
\[ CI = A - P \]
\[ CI = 25813.07 - 18400 \]
\[ CI \approx 7413.07 \] (approximately)

### Final Answer
The compound interest drawn on an amount of Rs. 18,400 at 12% per annum at the end of 3 years is approximately Rs. 7413.07.

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