Explanation:

Let's solve this step by step:

- The principal amount (P) is Rs7200.

- The amount (A) after one year is Rs7938.

- The interest is compounded half-yearly. This means two compounding periods in one year.

- The formula for compound interest is:

$$

A = P \left(1 + \frac{r}{2 \times 100}\right)^{2 \times n}

$$

where \(r\) is the rate, and \(n\) is the number of years.

- Plug in the values:

$$

7938 = 7200 \left(1 + \frac{r}{200}\right)^{2}

$$

- Simplifying, we get:

$$

\frac{7938}{7200} = \left(1 + \frac{r}{200}\right)^{2}

$$

- Solve for \(r\):

$$

1.1025 = \left(1 + \frac{r}{200}\right)^2

$$

Taking the square root:

$$

1.05 = 1 + \frac{r}{200}

$$

$$

\frac{r}{200} = 0.05

$$

$$

r = 10

$$

- This means the interest rate is 10% per annum.

- Option 1: 5% - Not the correct rate.

- Option 2: 8% - Still not the correct rate.

- Option 3: 12% - Higher than the calculated rate.

- Option 4: 10% - Matches the calculation.