Find the compound Interest on Rs. 32000 at 20% per annum for 1 year, compounded half yearly.

Options

A. Rs. 6320
B. Rs. 6720
C. Rs. 6400
D. Rs. 6500

Answer

To find the compound interest on Rs. 32,000 at 20% per annum for 1 year, compounded half-yearly, we can follow these steps:

### Step 1: Understand the Compounding Frequency
Since the interest is compounded half-yearly, we need to adjust the rate and time:
- The annual interest rate is 20%, so the half-yearly rate (r) will be:
\[ r = \frac{20}{2} = 10\% \]
- The time period (t) for 1 year compounded half-yearly will be:
\[ t = 2 \text{ half-years} \]

### Step 2: Use the Compound Interest Formula
The formula to calculate the amount (A) after compounding is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
Where:
- \(P\) = Principal amount (Rs. 32,000)
- \(r\) = Rate of interest per period (10%)
- \(n\) = Number of compounding periods (2)

### Step 3: Substitute the Values into the Formula
Now substituting the values into the formula:
\[ A = 32000 \left(1 + \frac{10}{100}\right)^2 \]
\[ A = 32000 \left(1 + 0.10\right)^2 \]
\[ A = 32000 \left(1.10\right)^2 \]

### Step 4: Calculate \( (1.10)^2 \)
Calculating \( (1.10)^2 \):
\[ (1.10)^2 = 1.21 \]

### Step 5: Calculate the Amount
Now, substituting back into the equation:
\[ A = 32000 \times 1.21 \]
\[ A = 38720 \]

### Step 6: Calculate the Compound Interest
To find the compound interest (CI), we subtract the principal from the total amount:
\[ CI = A - P \]
\[ CI = 38720 - 32000 \]
\[ CI = 6720 \]

### Final Answer
The compound interest on Rs. 32,000 at 20% per annum for 1 year, compounded half-yearly, is Rs. 6,720.

---