If `Rs 12000` is invested for two years at compound interest (compounded annually ) at the rate of `20%` per annum, then what is the interest ?

Options

A. `Rs 5280`
B. `Rs 5640`
C. `Rs 4280`
D. `Rs 4800`

Answer

To find the compound interest on an investment of Rs 12000 for two years at an annual interest rate of 20%, we can follow these steps:

### Step 1: Understand the formula for compound interest
The formula for calculating the amount \( A \) after \( n \) years with compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- \( P \) = principal amount (initial investment)
- \( r \) = annual interest rate (in percentage)
- \( n \) = number of years

### Step 2: Substitute the values into the formula
Here, \( P = 12000 \), \( r = 20 \), and \( n = 2 \). Plugging these values into the formula gives:
\[ A = 12000 \left(1 + \frac{20}{100}\right)^2 \]

### Step 3: Simplify the expression inside the parentheses
Calculating \( \frac{20}{100} \) gives \( 0.2 \), so:
\[ A = 12000 \left(1 + 0.2\right)^2 = 12000 \left(1.2\right)^2 \]

### Step 4: Calculate \( (1.2)^2 \)
Calculating \( (1.2)^2 \):
\[ (1.2)^2 = 1.44 \]
Thus, we have:
\[ A = 12000 \times 1.44 \]

### Step 5: Calculate the total amount \( A \)
Now, calculate \( 12000 \times 1.44 \):
\[ A = 17280 \]

### Step 6: Calculate the compound interest
The compound interest \( CI \) is given by:
\[ CI = A - P \]
Substituting the values:
\[ CI = 17280 - 12000 = 5280 \]

### Final Answer
The compound interest earned on the investment is Rs 5280.

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