What is the difference between the compound interests on ₹10000 for two years at 20% per annum when the interests are compounded half-yearly and yearly respectively?

When the interest is compounded yearly, then interest after 2 years = 10000 of 120% of 120% - 10000

= $$10000\times1.2\times1.2-10000$$

= $$10000\times(1.44-1)$$

= $$10000\times 0.44$$

= 4400

When the interest is compounded half-yearly, then interest after 2 years = 10000 of 110% of 110% of 110% of 110% - 10000 [In half-yearly, the rate of interest will be half and time will be double.]

= $$10000\times1.1\times1.1\times1.1\times1.1-10000$$
= $$10000\times(1.4641-1)$$

= $$10000\times0.4641$$

= 4641

Difference = 4641-4400 = ₹241