Find the amount and C.I. on Rs. 12,000 in one year at 10% per annum compounded half-yearly.

Answer

To find the amount and compound interest (C.I.) on Rs. 12,000 in one year at 10% per annum compounded half-yearly, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs. 12,000
- Rate of interest (R) = 10% per annum
- Time (T) = 1 year

### Step 2: Adjust the rate and time for half-yearly compounding
Since the interest is compounded half-yearly:
- The rate for half-yearly compounding (R/2) = 10% / 2 = 5%
- The number of compounding periods (N) = 2 * T = 2 * 1 = 2

### Step 3: Use the compound interest formula
The formula for the amount (A) when compounded is:
\[ A = P \left(1 + \frac{R}{100}\right)^N \]

### Step 4: Substitute the values into the formula
Substituting the values we have:
\[ A = 12,000 \left(1 + \frac{5}{100}\right)^2 \]

### Step 5: Simplify the expression
Calculating inside the bracket:
\[ A = 12,000 \left(1 + 0.05\right)^2 \]
\[ A = 12,000 \left(1.05\right)^2 \]

Now calculate \( (1.05)^2 \):
\[ (1.05)^2 = 1.1025 \]

So now we have:
\[ A = 12,000 \times 1.1025 \]

### Step 6: Calculate the amount
Calculating the final amount:
\[ A = 12,000 \times 1.1025 = 13,230 \]

### Step 7: Calculate the compound interest (C.I.)
The compound interest can be calculated as:
\[ C.I. = A - P \]
\[ C.I. = 13,230 - 12,000 = 1,230 \]

### Final Results
- Amount (A) = Rs. 13,230
- Compound Interest (C.I.) = Rs. 1,230

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