Correct Answer: INR 1576.25

Solution : Rate, $R$ = 10%
Term, $n$ = 1 year
Principal sum, $P$ = INR 10000
When compounded half-yearly,
Amount = $P(1+\frac{R}{200})^{2n}$
Compound interest = $P(1+\frac{R}{200})^{2n}-P$
= $10000(1+\frac{10}{200})^{2×1.5}-10000$
= $10000(1+\frac{1}{20})^{3}-10000$
= $10000(\frac{21}{20})^{3}-10000$
= $10000(\frac{21^3}{20^3}-1)$
= $10000(\frac{21^3-20^3}{8000})$
= $\frac{10000×(441+400+420)×1}{8000}$
= $\frac{12610}{8}$
= INR $1576.25$
Hence, the correct answer is INR 1576.25.