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4024/22 Oct/Nov 2025, Question 16: Compound Interest

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 6 marks

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The question, in short

Population falls exponentially by x% yearly from 120000 on 1 January 2020 to 102885 on 1 January 2023; then grows at 1.6% yearly. Find x and the year population first exceeds 120000.

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Part (a) · 3 marks

Using the three-year decrease from 120000 to 102885, find the annual percentage decrease x.

  1. 1120 000 × k³ = 102 885, so k³ = 102 885/120 000 = 0.857375
  2. 2k = ∛0.857375 = 0.95
  3. 3Decrease of 1 − 0.95 = 0.05, so x = 5

Answer5

Part (b) · 3 marks

From 102885 growing at 1.6% per year, find the first 1 January when the population exceeds 120000.

  1. 1Population n years after 2023 = 102 885 × 1.016ⁿ
  2. 2n = 9: 102 885 × 1.016⁹ = 118 685 (less than 120 000)
  3. 3n = 10: 102 885 × 1.016¹⁰ = 120 584 (more than 120 000)
  4. 4Year = 2023 + 10 = 2033

Answer2033

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