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The problem in the image is asking to calculate the compound interest on an amount of ₹62,500 for \( 1 \frac{1}{2} \) years at an annual interest rate of 8%, compounded semi-annually.

### Key details:
- **Principal (P)** = ₹62,500
- **Time (T)** = \( 1 \frac{1}{2} \) years = 1.5 years
- **Annual Interest Rate (R)** = 8%
- **Compounding Frequency** = Semi-annually (2 times per year)

### Step-by-step solution:
1. **Convert the interest rate and time for semi-annual compounding:**
   - Semi-annual rate \( R_{semi} = \frac{8}{2} = 4\%\)
   - Time in terms of semi-annual periods \( T_{semi} = 1.5 \times 2 = 3 \) periods

2. **Use the Compound Interest formula:**
   \[
   A = P \left( 1 + \frac{R_{semi}}{100} \right)^{T_{semi}}
   \]
   Where:
   - \( A \) is the amount after interest
   - \( P \) is the principal
   - \( R_{semi} \) is the semi-annual interest rate (4%)
   - \( T_{semi} \) is the number of semi-annual periods (3)

   Substituting the values:
   \[
   A = 62,500 \left( 1 + \frac{4}{100} \right)^3
   \]
   \[
   A = 62,500 \left( 1 + 0.04 \right)^3 = 62,500 \times (1.04)^3
   \]
   \[
   A = 62,500 \times 1.124864
   \]
   \[
   A = 70,304
   \]

3. **Calculate the compound interest:**
   \[
   \text{Compound Interest} = A - P = 70,304 - 62,500 = 7,804
   \]

### Final Answer:
The compound interest is **₹7,804**.

Let me know if you need more details or have any questions.

Here are 5 related questions:
1. What is the formula for compound interest compounded quarterly?
2. How does the number of compounding periods affect the final amount?
3. What is the difference between simple interest and compound interest?
4. How would the interest change if it were compounded annually instead of semi-annually?
5. What is the formula to calculate the future value of an investment?

**Tip:** For compound interest, the more frequent the compounding, the greater the total interest accumulated over time.

Calculate the compound interest on ₹62,500 for 1.5 years at an 8% annual interest rate, compounded semi-annually.

Solve a compound interest problem where ₹62,500 is invested for 1.5 years at an 8% annual rate compounded semi-annually. The solution uses the compound interest formula and provides a step-by-step breakdown. Suitable for high school students.

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