Explanation:

To find the compound interest, let's go through the steps:

- Principal Amount (P): Rs 22,500

- Annual Interest Rate (R): 16%

- Time (T): 1 year

- Compounding Frequency: Half-yearly

1. Effective Period: 1 year = 2 half-years

2. Rate per Period (R/2): 16% / 2 = 8% or 0.08

3. Compound Interest Formula:

$$

A = P \left(1 + \frac{R}{n}\right)^{nT}

$$

where \(A\) is the amount, \(n\) is the number of times interest applied per time period.

4. Substitution and Calculation:

$$

A = 22500 \left(1 + \frac{0.08}{1}\right)^{2}

$$

$$

A = 22500 \times 1.08 \times 1.08

$$

$$

A = 22500 \times 1.1664 = 26244

$$

5. Compound Interest (A - P):

$$

CI = 26244 - 22500 = 3744

$$

- Option 1: Rs 3,744 \(\color{green}\checkmark\)

- Option 2: Rs 3,700

- Option 3: Rs 3,600

- Option 4: Rs 36,244

Correct Answer: Option 1: Rs 3,744