The amount and the compound Interest on Rs. 24000 compounded semi-annually for `1 (1)/(2)`yr at the rate of 10% per annum are

Options

A. Rs. 27000, Rs. 3774
B. Rs. 27783, Rs. 3583
C. Rs. 27000, Rs. 3780
D. Rs. 27783, Rs. 3783

Answer

To solve the problem of finding the amount and compound interest on Rs. 24000 compounded semi-annually for 1.5 years at a rate of 10% per annum, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Principal (P) = Rs. 24000
- Rate (R) = 10% per annum
- Time (T) = 1.5 years

2. **Adjust the Time and Rate for Semi-Annual Compounding:**
- Since the interest is compounded semi-annually, we need to adjust the time and rate:
- The time in semi-annual periods = 1.5 years × 2 = 3 periods
- The rate per period = 10% / 2 = 5% per period

3. **Use the Compound Interest Formula:**
- The formula for the amount (A) when compounded is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
- Where:
- \( P \) = Principal
- \( R \) = Rate per period
- \( n \) = Number of compounding periods

4. **Substitute the Values into the Formula:**
- Here, \( P = 24000 \), \( R = 5\% \), and \( n = 3 \):
\[ A = 24000 \left(1 + \frac{5}{100}\right)^3 \]
- Simplifying this gives:
\[ A = 24000 \left(1 + 0.05\right)^3 = 24000 \left(1.05\right)^3 \]

5. **Calculate \( (1.05)^3 \):**
- \( (1.05)^3 = 1.157625 \)

6. **Calculate the Amount (A):**
- Now substitute back to find A:
\[ A = 24000 \times 1.157625 \approx 27783 \]

7. **Calculate the Compound Interest (CI):**
- The formula for compound interest is:
\[ CI = A - P \]
- Substituting the values gives:
\[ CI = 27783 - 24000 = 3783 \]

### Final Results:
- **Amount (A)** = Rs. 27783
- **Compound Interest (CI)** = Rs. 3783