Calculate the amount and the compound interest on Rs. 8,000 for 1 year at 10% per annum compounded half-yearly.

Answer

To solve the problem of calculating the amount and the compound interest on Rs. 8,000 for 1 year at 10% per annum compounded half-yearly, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Principal (P) = Rs. 8,000
- Rate of interest (R) = 10% per annum
- Time (T) = 1 year

2. **Adjust the rate and time for half-yearly compounding**:
- Since the interest is compounded half-yearly, we need to adjust the rate and the time:
- The effective rate for half-yearly compounding (r) = R / 2 = 10% / 2 = 5%
- The number of compounding periods (n) = 2 * T = 2 * 1 = 2

3. **Use the compound interest formula**:
- The formula for calculating the amount (A) in compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]
- Substituting the values:
\[ A = 8000 \left(1 + \frac{5}{100}\right)^2 \]

4. **Simplify the expression**:
- Calculate \(1 + \frac{5}{100} = 1 + 0.05 = 1.05\)
- Now substitute this value into the formula:
\[ A = 8000 \times (1.05)^2 \]

5. **Calculate \((1.05)^2\)**:
- \((1.05)^2 = 1.1025\)

6. **Calculate the amount (A)**:
- Now substitute back to find A:
\[ A = 8000 \times 1.1025 = 8820 \]
- Therefore, the total amount after 1 year is Rs. 8,820.

7. **Calculate the compound interest (CI)**:
- The formula for compound interest is:
\[ CI = A - P \]
- Substituting the values:
\[ CI = 8820 - 8000 = 820 \]
- Therefore, the compound interest is Rs. 820.

### Final Results:
- Amount (A) = Rs. 8,820
- Compound Interest (CI) = Rs. 820