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CA Foundation · Quantitative Aptitude · Sequence and Series

An investment portfolio generates returns following an infinite geometric series. The first-year return is ₹50,000 and each subsequent year's return is 75% of the previous year's return. What is the total return the investor can expect to receive indefinitely?

The total expected return is ₹200,000. Using the infinite geometric series formula S = a/(1−r) with first term ₹50,000 and common ratio 0.75, we get S = 50,000/0.25 = ₹200,000.

  1. A₹150,000
  2. B₹200,000Correct
  3. C₹250,000
  4. D₹300,000

Explanation

For an infinite geometric series where |r| < 1, the sum is S = a/(1-r). Here a = 50,000 and r = 0.75. Therefore S = 50,000/(1 - 0.75) = 50,000/0.25 = ₹200,000. Option ₹250,000 results from incorrectly using r = 0.8 in the formula. The condition |r| < 1 ensures convergence.

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