CAT 2025 Slot 1 QA Q6 Interest

Question 6 of the Quantitative Ability (QA) section, CAT 2025 Slot 1, with CAT's official answer and a worked solution.

At a certain simple rate of interest, a given sum amounts to Rs 13920 in 3 years, and to Rs 18960 in 6 years and 6 months. If the same given sum had been invested for 2 years at the same rate as before but with interest compounded every 6 months, then the total interest earned, in rupees, would have been nearest to
  1. A
    3096
  2. B
    3150
  3. C
    3180
  4. D
    3221

Answer: (D) 3221 Interest MCQ

Solution

  1. Interest for \(6.5 - 3 = 3.5\) years \(= 18960 - 13920 = 5040\), so the yearly interest is \(1440\).
  2. Principal \(= 13920 - 3 \times 1440 = 9600\); rate \(= \frac{1440}{9600} = 15\%\).
  3. Half-yearly compounding: 4 periods at \(7.5\%\). \(1.075^2 = 1.155625\), and \(1.155625^2 \approx 1.33547\).
  4. Interest \(\approx 9600 \times 0.33547 \approx 3220.5\), nearest to 3221.

Same concept in other years

See every question on Comparing simple and compound interest on the same principal.

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