What is the difference (in ₹) between the compound interest, when interest is compounded 6-monthly, and the simple interest on a sum of ₹10,000 for $$1\frac{1}{2}$$ years at 10% p.a.?

If interest is half-yearly, Then 

Time = $$1.5\times\ 2=3$$

Rate = $$\frac{10}{2}=\ 5\%$$

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

= $$A=10,000\left(1+\frac{5}{100}\right)^3$$

$$A=10,000\ \times\ \frac{21}{20}\times\ \frac{21}{20}\times\ \frac{21}{20}=11576.25$$

C.I = A - P = 11576.25 - 10000 = ₹1576.35

Simple Interest = $$S.I\ =\frac{\left(P\times\ R\times\ T\right)}{100}$$

= $$\frac{\left(10000\times\ 10\times\ 1.5\right)}{100}$$

= ₹1500

Required Difference = ₹1576.25 - ₹1500 = ₹76.25

Hence, Option C is correct.