The compound interest on `Rs. 24000` at `10%` per annum for `1(1)/2` years, Interest being compounded semi-annually is:

Options

A. `Rs. 3783 `
B. `Rs. 3777 `
C. `Rs. 3780 `
D. `Rs. 3781`

Answer

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

### Step 1: Identify the parameters
- Principal (P) = Rs. 24000
- Rate of interest (R) = 10% per annum
- Time (T) = 1.5 years

### Step 2: Adjust the rate and time for semi-annual compounding
Since the interest is compounded semi-annually:
- The effective rate per half year = 10% / 2 = 5%
- The number of compounding periods in 1.5 years = 1.5 years * 2 = 3 periods

### Step 3: Use the compound interest formula
The formula for compound interest is given by:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
Where:
- A = the amount after n periods
- P = principal amount
- R = rate of interest per period
- n = number of compounding periods

Substituting the values:
- P = 24000
- R = 5%
- n = 3

\[ A = 24000 \left(1 + \frac{5}{100}\right)^3 \]
\[ A = 24000 \left(1 + 0.05\right)^3 \]
\[ A = 24000 \left(1.05\right)^3 \]

### Step 4: Calculate \( (1.05)^3 \)
Calculating \( (1.05)^3 \):
\[ (1.05)^3 = 1.157625 \]

### Step 5: Calculate the total amount (A)
Now, substituting back into the formula:
\[ A = 24000 \times 1.157625 \]
\[ A \approx 27783 \]

### Step 6: Calculate the compound interest (CI)
The compound interest is given by:
\[ CI = A - P \]
\[ CI = 27783 - 24000 \]
\[ CI \approx 3783 \]

### Final Answer
The compound interest on Rs. 24000 at 10% per annum for 1.5 years, compounded semi-annually, is approximately Rs. 3783.

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