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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 on a sum of money is increased by what percentage if the interest is compounded half-yearly instead of annually, keeping the same rate of interest of 8% for 2 years? Quantity B: A man borrowed a sum of money at a simple interest of 8% per annum for 6 years. By how much percentage will the interest increase, if he clears his debt after 74 months?

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 on a sum of money is increased by what percentage if the interest is compounded half-yearly instead of annually, keeping the same rate of interest of 8% for 2 years? Quantity B: A man borrowed a sum of money at a simple interest of 8% per annum for 6 years. By how much percentage will the interest increase, if he clears his debt after 74 months? Correct Answer Quantity A < Quantity B

Solving for Quantity A:

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

Compound interest = P

⇒ CI = P

⇒ CI = P(1.1664 - 1)

⇒ CI = 0.1664P

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(1.1699 - 1)

⇒ CI = 0.1699P

Hence, percentage increase = × 100 = 2.1%

⇒ Quantity A = 2.1%

Solving for Quantity B:

Simple interest after 6 years = (P × 8 × 6)/100 = 0.48P

Simple interest after 74 months = (P × 8 × 74)/(100 × 12) = 0.493P

Hence, percentage increase = × 100 = 2.7%

⇒ Quantity B = 2.7%

∴ Quantity A < Quantity B

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