Find the amount on Rs 3000 for `1 1/2 ` yr at 10 % per annum interest being compounded half- yearly .

Options

A. Rs `3183.24`
B. Rs `3472.88`
C. Rs `3352.15`
D. Rs `3096.44`

Answer

To find the amount on Rs. 3000 for 1.5 years at 10% per annum interest compounded half-yearly, we will follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 3000
- Rate of interest (R) = 10% per annum
- Time (T) = 1.5 years

### Step 2: Convert 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%
- Number of compounding periods (N) = 2 * T = 2 * 1.5 = 3

### Step 3: Use the compound interest formula
The formula for compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^N \]
Where:
- A = Amount after time T
- P = Principal
- R = Rate of interest per period
- N = Number of compounding periods

### Step 4: Substitute the values into the formula
Substituting the values we have:
\[ A = 3000 \left(1 + \frac{5}{100}\right)^3 \]

### Step 5: Calculate the expression inside the parentheses
\[ A = 3000 \left(1 + 0.05\right)^3 \]
\[ A = 3000 \left(1.05\right)^3 \]

### Step 6: Calculate \( (1.05)^3 \)
Calculating \( (1.05)^3 \):
\[ (1.05)^3 = 1.157625 \]

### Step 7: Multiply by the principal
Now substitute back into the equation:
\[ A = 3000 \times 1.157625 \]
\[ A = 3472.875 \]

### Step 8: Final amount
Thus, the amount after 1.5 years is approximately Rs. 3472.88.

### Summary of Steps:
1. Identify principal, rate, and time.
2. Adjust the rate and time for half-yearly compounding.
3. Use the compound interest formula.
4. Substitute the values and calculate.