Rs 10000 is being compounded at 20% per annum. Calculate the amount after 2 years if rate of interest is charged half yearly.
A. Rs 10041 B. Rs 14641 C. Rs 12000 D. Rs 13660

Options

A. C
B. D
C. A
D. B

Answer

To solve the problem of calculating the amount after 2 years when Rs. 10,000 is compounded at 20% per annum with interest charged half yearly, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Principal (P)**:
The principal amount is given as Rs. 10,000.

**Hint**: Always start by identifying the principal amount in compound interest problems.

2. **Determine the Annual Interest Rate (R)**:
The annual interest rate is 20%. Since the interest is compounded half yearly, we need to halve this rate.

\[ R = \frac{20\%}{2} = 10\% \]

**Hint**: When compounding is done more frequently than annually, divide the annual rate by the number of compounding periods per year.

3. **Calculate the Number of Compounding Periods (n)**:
Since the interest is compounded half yearly and we are looking at a period of 2 years, we need to calculate the total number of compounding periods.

\[ n = 2 \text{ years} \times 2 = 4 \text{ periods} \]

**Hint**: Multiply the number of years by the frequency of compounding to find the total number of compounding periods.

4. **Convert the Interest Rate to a Decimal**:
Convert the percentage rate to a decimal for calculation.

\[ r = \frac{10}{100} = 0.10 \]

**Hint**: Always convert percentages to decimals before performing calculations.

5. **Use the Compound Interest Formula**:
The formula for compound interest is:

\[ A = P \left(1 + r\right)^n \]

Substituting the values we have:

\[ A = 10000 \left(1 + 0.10\right)^4 \]

6. **Calculate the Amount**:
First, calculate \( (1 + 0.10)^4 \):

\[ (1 + 0.10)^4 = (1.10)^4 \]

Now calculate \( (1.10)^4 \):

\[ (1.10)^4 = 1.4641 \]

Now, multiply by the principal:

\[ A = 10000 \times 1.4641 = 14641 \]

**Hint**: When calculating powers, it can be helpful to break it down into smaller steps or use a calculator.

7. **Final Amount**:
The amount after 2 years is Rs. 14,641.

**Hint**: Always check your calculations to ensure accuracy.

### Conclusion:
The final amount after 2 years when Rs. 10,000 is compounded at 20% per annum half yearly is **Rs. 14,641**, which corresponds to option **B**.