Find the compound interest on Rs 15625 for `1(1)/(2)` years at 8% per annum when compounded half-yearly.

Answer

To find the compound interest on Rs 15625 for \(1 \frac{1}{2}\) years at 8% per annum when compounded half-yearly, we can follow these steps:

### Step 1: Identify the Principal, Rate, and Time
- **Principal (P)** = Rs 15625
- **Rate (R)** = 8% per annum
- **Time (T)** = \(1 \frac{1}{2}\) years = \(1.5\) years

### Step 2: Adjust the Rate and Time for Half-Yearly Compounding
Since the interest is compounded half-yearly:
- **Half-Yearly Rate** = \(\frac{8\%}{2} = 4\%\)
- **Total Half-Yearly Periods** = \(1.5 \text{ years} \times 2 = 3 \text{ half-years}\)

### Step 3: Use the Compound Interest Formula
The formula to calculate the amount \(A\) when compounded is:
\[ A = P \left(1 + \frac{R}{100}\right)^n \]
Where:
- \(P\) = Principal
- \(R\) = Rate of interest per period
- \(n\) = Number of compounding periods

Substituting the values:
\[ A = 15625 \left(1 + \frac{4}{100}\right)^3 \]

### 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:
\[ A = 15625 \times (1.04)^3 \]

Next, calculate \( (1.04)^3 \):
\[ (1.04)^3 = 1.04 \times 1.04 \times 1.04 = 1.124864 \]

Now calculate the amount:
\[ A = 15625 \times 1.124864 \approx 17656.00 \]

### Step 5: Calculate the Compound Interest
The compound interest (CI) is calculated as:
\[ CI = A - P \]
Substituting the values:
\[ CI = 17656.00 - 15625 = 2011.00 \]

### Final Answer
The compound interest on Rs 15625 for \(1 \frac{1}{2}\) years at 8% per annum when compounded half-yearly is **Rs 2011.00**.

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