The compound interest formula, compounded semi-annually, is:
\[\nA = P \left( 1 + \frac{r}{2} \right)^{2t}\n\]
where:
- \( P = 24,000 \) (principal),
- \( r = 10% = 0.10 \) (interest rate),
- \( t = 1 \frac{1}{2} = 1.5 \) (years).
Calculate \( A \):
\[\nA = 24000 \left( 1 + \frac{0.10}{2} \right)^{2 \times 1.5} = 24000 \left( 1.05 \right)^{3}\n\]
\[\nA = 24000 \times 1.157625 = 27,786\n\]
Compound interest (\( CI \)) is:
\[\nCI = A - P = 27,786 - 24,000 = ₹ 3,786\n\]
The answer is ₹ 3,780 (approximate).