CAT 2025 Slot 2 QA Q18 Interest

Question 18 of the Quantitative Ability (QA) section, CAT 2025 Slot 2, with CAT's official answer and a worked solution.

A loan of Rs 1000 is fully repaid by two installments of Rs 530 and Rs 594, paid at the end of first and second year, respectively. If the interest is compounded annually, then the rate of interest, in percentage, is
  1. A
    8
  2. B
    10
  3. C
    11
  4. D
    9

Answer: (A) 8 Interest MCQ

Solution

  1. Present values must add to the loan: \(\frac{530}{1+r} + \frac{594}{(1+r)^2} = 1000\).
  2. Try \(r = 8\%\): \(\frac{530}{1.08} = 490.74\), \(\frac{594}{1.1664} = 509.26\); sum \(= 1000\).
  3. Rate \(= 8\%\).

Shortcut. Equivalently, \(1000 \times 1.08 = 1080\); after paying 530, \(550 \times 1.08 = 594\).

Same concept in other years

See every question on Loan repaid in instalments under compound interest.

More Interest questions from CAT

All 19 Interest questions asked since 2017.