What would be the C.I. obtained on an amount of rs. 12000 at the rate of 9% p.a. for 3 years?

Options

A. a. rs.3840
B. b. rs.3740.75
C. c. rs.3540
D. d. rs.3640

Answer

To find the compound interest (C.I.) on an amount of Rs. 12,000 at the rate of 9% per annum for 3 years, we can follow these steps:

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

### Step 2: Substitute the values into the formula
Given:
- \(P = 12000\)
- \(R = 9\)
- \(n = 3\)

Substituting these values into the formula:
\[ C.I. = 12000 \left(1 + \frac{9}{100}\right)^3 - 12000 \]

### Step 3: Simplify the expression inside the parentheses
Calculate \(1 + \frac{9}{100}\):
\[ 1 + \frac{9}{100} = 1 + 0.09 = 1.09 \]

### Step 4: Raise the result to the power of 3
Now we need to calculate \(1.09^3\):
\[ 1.09^3 = 1.09 \times 1.09 \times 1.09 \]
Calculating this step-by-step:
- First, calculate \(1.09 \times 1.09 = 1.1881\)
- Then, multiply that result by \(1.09\):
\[ 1.1881 \times 1.09 \approx 1.295029 \]

### Step 5: Substitute back into the formula
Now substitute \(1.09^3\) back into the compound interest formula:
\[ C.I. = 12000 \times 1.295029 - 12000 \]

### Step 6: Calculate the total amount
Now calculate \(12000 \times 1.295029\):
\[ 12000 \times 1.295029 \approx 15540.348 \]

### Step 7: Subtract the principal from the total amount
Now, we subtract the principal amount from this result to find the compound interest:
\[ C.I. = 15540.348 - 12000 \approx 3540.348 \]

### Step 8: Round off to the nearest whole number
Since we are dealing with currency, we can round this to:
\[ C.I. \approx 3540 \]

### Final Answer
The compound interest obtained on an amount of Rs. 12,000 at the rate of 9% per annum for 3 years is Rs. 3540.

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