CAT 2024 Slot 2 QA Q15 Interest

Question 15 of the Quantitative Ability (QA) section, CAT 2024 Slot 2, with CAT's official answer and a worked solution.

Anil invests Rs 22000 for 6 years in a scheme with 4% interest per annum, compounded half-yearly. Separately, Sunil invests a certain amount in the same scheme for 5 years, and then reinvests the entire amount he receives at the end of 5 years, for one year at 10% simple interest. If the amounts received by both at the end of 6 years are equal, then the initial investment, in rupees, made by Sunil is
  1. A
    20480
  2. B
    20808
  3. C
    20640
  4. D
    20860

Answer: (B) 20808 Interest MCQ

Solution

  1. Half-yearly rate 2%. Anil: \(22000 \times 1.02^{12}\).
  2. Sunil with principal \(P\): \(P \times 1.02^{10} \times 1.10\).
  3. Equating: \(P = \frac{22000 \times 1.02^2}{1.1} = 20000 \times 1.0404 = 20808\).

Shortcut. Cancel \(1.02^{10}\) on both sides before computing.

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