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In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and choose the correct option. Quantity A: The compound interest (compounded half-yearly) on a sum of money is what percentage of the sum at a rate of 10% per annum after 2 years? Quantity B: The compound interest (compounded quarterly) on a sum of money is what percentage of the sum at a rate of 10% per annum after 2 years?

In the following question, two statements are numbered as A and B. On solving these statements we get quantities A and B respectively. Solve for the both quantities and choose the correct option. Quantity A: The compound interest (compounded half-yearly) on a sum of money is what percentage of the sum at a rate of 10% per annum after 2 years? Quantity B: The compound interest (compounded quarterly) on a sum of money is what percentage of the sum at a rate of 10% per annum after 2 years? Correct Answer Quantity A < Quantity B

Solving for Quantity A:

When the compound interest is compounded half-yearly, on a sum of Rs. P at a rate of R% after T years, then,

Compound interest = P

⇒ CI = P

⇒ CI = P(1.2155 - 1)

⇒ CI = 0.2155P

⇒ CI = 21.55% of P

⇒ Quantity A = 21.55%

Solving for Quantity B:

When the compound interest is compounded quarterly, on a sum of Rs. P at a rate of R% after T years, then,

Compound interest = P

⇒ CI = P

⇒ CI = P(1.2184 - 1)

⇒ CI = 0.2184P

⇒ CI = 21.84% of P

⇒ Quantity B = 21.84%

∴ Quantity A < Quantity B

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