What is the principal amount which earns Rs. 132 compound interest for the second year at `10%` per annum

Options

A. Rs.1000
B. Rs.1200
C. Rs.1320
D. None of these

Answer

To find the principal amount that earns Rs. 132 as compound interest for the second year at an interest rate of 10% per annum, we can follow these steps:

### Step 1: Understand the concept of compound interest
In compound interest, the interest for each year is calculated on the principal amount plus the interest accumulated from previous years. The interest earned in the second year is based on the total amount after the first year.

### Step 2: Set up the formula for compound interest
The formula for compound interest for the second year can be expressed as:
\[ \text{CI}_{\text{second year}} = \text{Principal} \times \left(1 + \frac{r}{100}\right) \times \frac{r}{100} \]
Where:
- \( \text{CI}_{\text{second year}} \) is the compound interest earned in the second year.
- \( r \) is the rate of interest (10% in this case).

### Step 3: Substitute the known values
We know that the compound interest for the second year is Rs. 132 and the rate \( r = 10 \):
\[ 132 = P \times \left(1 + \frac{10}{100}\right) \times \frac{10}{100} \]

### Step 4: Simplify the equation
First, simplify the term \( \left(1 + \frac{10}{100}\right) \):
\[ 1 + \frac{10}{100} = 1 + 0.1 = 1.1 \]
Now, substitute this back into the equation:
\[ 132 = P \times 1.1 \times 0.1 \]
\[ 132 = P \times 0.11 \]

### Step 5: Solve for the principal amount \( P \)
Now, isolate \( P \):
\[ P = \frac{132}{0.11} \]
\[ P = 1200 \]

### Conclusion
The principal amount that earns Rs. 132 as compound interest for the second year at 10% per annum is Rs. 1200.

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