The compound interest on Rs. 6000 for `1 1/2` years at `10%` per annum, the interest being paid half yearly, will be-

Options

A. Rs. `912cdot75`
B. Rs. 930
C. Rs. `932cdot50`
D. Rs. `945cdot75`

Answer

To find the compound interest on Rs. 6000 for 1.5 years at an interest rate of 10% per annum, compounded half-yearly, we can follow these steps:

### Step 1: Identify the Principal, Rate, and Time
- Principal (P) = Rs. 6000
- Annual Rate of Interest (R) = 10%
- Time (T) = 1.5 years

### Step 2: Adjust the Rate and Time for Half-Yearly Compounding
Since the interest is compounded half-yearly, we need to adjust the rate and time:
- Half-yearly Rate = R/2 = 10%/2 = 5%
- Total Time in Half-Years = 1.5 years × 2 = 3 half-years

### 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:
- \( A \) = Amount after time \( n \)
- \( P \) = Principal
- \( r \) = Rate of interest per period
- \( n \) = Number of compounding periods

Substituting the values:
- \( P = 6000 \)
- \( r = 5 \)
- \( n = 3 \)

### Step 4: Calculate the Amount
Now, substituting the values into the formula:
\[ A = 6000 \left(1 + \frac{5}{100}\right)^3 \]
\[ A = 6000 \left(1 + 0.05\right)^3 \]
\[ A = 6000 \left(1.05\right)^3 \]

Now, calculate \( (1.05)^3 \):
\[ (1.05)^3 = 1.157625 \]

Now, calculate \( A \):
\[ A = 6000 \times 1.157625 \]
\[ A = 6945.75 \]

### Step 5: Calculate the Compound Interest
To find the compound interest (CI), we subtract the principal from the amount:
\[ CI = A - P \]
\[ CI = 6945.75 - 6000 \]
\[ CI = 945.75 \]

### Final Answer
The compound interest on Rs. 6000 for 1.5 years at 10% per annum, compounded half-yearly, is Rs. 945.75.