CA Foundation · Quantitative Aptitude · Sequence and Series
A recurring annual royalty from a patent is ₹90,000 in the first year, and each later year's royalty is two-thirds of the previous year's royalty, continuing indefinitely. What is the total royalty receivable over all years, ignoring the time value of money?
The total royalty is ₹2,70,000. The royalty forms an infinite geometric series with first term 90,000 and common ratio two-thirds, so the sum is 90,000 divided by (1 minus two-thirds), which is 90,000 times 3, or 2,70,000.
- A₹2,70,000Correct
- B₹1,80,000
- C₹1,35,000
- D₹3,60,000
Explanation
The series is a GP with a = 90,000 and r = 2/3. S = a/(1 - r) = 90,000/(1/3) = 2,70,000. Check: second year is 60,000 and 90,000 × 3 = 2,70,000. The value 1,80,000 results from dividing by (1 - r) wrongly as 1/2.
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