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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: At what rate percent per annum will the simple interest on a sum of Rs. 50000 after 4 years is Rs. 16000? Quantity B: At what rate percent per annum will the interest compounded annually on a sum after 2 years is 10.25% of the sum?

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: At what rate percent per annum will the simple interest on a sum of Rs. 50000 after 4 years is Rs. 16000? Quantity B: At what rate percent per annum will the interest compounded annually on a sum after 2 years is 10.25% of the sum? Correct Answer Quantity A > Quantity B

Solving for Quantity A:

Let the rate be R% per annum

∵ Simple interest = (Principal × Rate × Time)/100

⇒ 16000 = (50000 × R × 4)/100

⇒ R = 16000/2000 = 8%

⇒ Quantity A = 8%

Solving for Quantity B:

Let the rate be R% per annum and the sum be Rs. P

∵ Compound interest = Principal ×

⇒ 10.25% of P = P ×

⇒ 0.1025 = (1 + R/100)2 – 1

⇒ (1 + R/100)2 = 1.1025

⇒ 1 + R/100 = 1.05

⇒ R/100 = 0.05

⇒ R = 5%

⇒ Quantity B = 5%

∴ Quantity A > Quantity B

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