Explanation:

- The principal amount is Rs. 8000.

- The interest rate is 10% per annum, but it is compounded half-yearly. Therefore, the half-yearly rate is 5%.

- The formula for compound interest is:

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

where:

\( A \) is the amount,

\( P \) is the principal (Rs. 8000),

\( r \) is the annual interest rate (10% or 0.10),

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

\( t \) is the time in years (0.5 for 6 months).

- Calculate:

$$ A = 8000 \left(1 + \frac{0.10}{2}\right)^{2 \times 0.5} $$

$$ A = 8000 \times 1.05 $$

$$ A = 8400 $$

- The compound interest is:

$$ \text{Compound Interest} = A - P = 8400 - 8000 = 400 $$

- Option 4: Rs. 400 is the correct answer.