CAT 2024 Slot 3 QA Q11 Interest

Question 11 of the Quantitative Ability (QA) section, CAT 2024 Slot 3, with CAT's official answer and a worked solution.

Aman invests Rs 4000 in a bank at a certain rate of interest, compounded annually. If the ratio of the value of the investment after 3 years to the value of the investment after 5 years is 25 : 36, then the minimum number of years required for the value of the investment to exceed Rs 20000 is

TITA: type in the answer. There are no options and no negative marking.

Answer: 9 Interest TITA

Solution

  1. \(\frac{A_3}{A_5} = \frac{1}{(1+r)^2} = \frac{25}{36}\), so \(1 + r = 1.2\).
  2. Need \(4000 \times 1.2^n > 20000\), i.e. \(1.2^n > 5\).
  3. \(1.2^8 \approx 4.30\), \(1.2^9 \approx 5.16\). So 9 years.

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