Explanation:

To calculate compound interest compounded half-yearly, you must:

- Split the annual interest rate in half. Here, 10% annually becomes 5% semi-annually.

- This means you will have two compounding periods in a year.

- Use the formula for compound interest:

$$A=P{(1+\frac{r}{n})}^{nt}$$

Where:

- $A$ is the final amount.

- $P$ is the principal amount (80,000).

- $r$ is the annual interest rate (0.10).

- $n$ is the number of compounding periods per year (2 for half-yearly).

- $t$ is the time in years (1 in this case).

- Now plug in the values:

$$A=80,000{(1+\frac{0.10}{2})}^{2\times 1}$$

$$A=80,000{(1+0.05)}^2$$

$$A=80,000\times (1.05{)}^2$$

$$A=80,000\times 1.1025$$

$$A=88,200$$

- Compound interest = Final amount - Principal = 88,200 - 80,000 = 8,200

- Therefore, the compound interest is Rs8,200.

- Option 2: Rs8,200