Find the compound interest on Rs 48,000 for one year at 8% per annum when compounded half yearly.

Answer

To find the compound interest on Rs 48,000 for one year at 8% per annum when compounded half yearly, we can follow these steps:

### Step 1: Identify the values
- Principal (P) = Rs 48,000
- Rate of interest (R) = 8% per annum
- Time (T) = 1 year

### Step 2: Convert the rate and time for half-yearly compounding
Since the interest is compounded half yearly:
- The rate for half a year = 8% / 2 = 4%
- The time in half years = 1 year = 2 half years

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

Substituting the values:
- \( P = 48,000 \)
- \( R = 4 \) (since we are using the half-yearly rate)
- \( n = 2 \)

So, we have:
\[ A = 48,000 \left(1 + \frac{4}{100}\right)^2 \]

### Step 4: Calculate the amount
First, simplify the expression inside the parentheses:
\[ 1 + \frac{4}{100} = 1 + 0.04 = 1.04 \]

Now substitute this back into the formula:
\[ A = 48,000 \times (1.04)^2 \]

Calculating \( (1.04)^2 \):
\[ (1.04)^2 = 1.0816 \]

Now calculate the amount:
\[ A = 48,000 \times 1.0816 = 51,916.8 \]

### Step 5: Calculate the compound interest
The compound interest (CI) is given by:
\[ CI = A - P \]
Substituting the values we found:
\[ CI = 51,916.8 - 48,000 = 3,916.8 \]

### Final Answer
The compound interest on Rs 48,000 for one year at 8% per annum when compounded half yearly is **Rs 3,916.80**.

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