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0580/42 Oct/Nov 2023, Question 3: Simple Interest

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 15 marks

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The question, in short

Work with percentage change, simple and compound interest, and exponential decay: find car values, Ali's investment, Sara's rate r, and radioactive mass decreases.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (ai) · 2 marks

Calculate the car's value after one year given a 10% yearly decrease from $7695.

  1. 17695 × (100 − 10)/100 = 7695 × 0.9
  2. 2= $6925.50

Answer6925.50

Part (aii) · 2 marks

Calculate the car's value one year ago, knowing it decreased 10% to $7695.

  1. 1X × 0.9 = 7695
  2. 2X = 7695 ÷ 0.9 = $8550

Answer8550

Part (b) · 3 marks

Calculate the value of $600 invested at 2% per year simple interest after 5 years.

  1. 1Interest = 600 × 2 × 5/100 = 60
  2. 2Value = 600 + 60 = $660

Answer660

Part (c) · 3 marks

Find r when $500 grows to $601.35 over 12 years at r% compound interest.

  1. 1500 × (1 + r/100)¹² = 601.35
  2. 21 + r/100 = ¹²√(601.35/500) = 1.01549…
  3. 3r = 1.549… ≈ 1.55

Answer1.55 or 1.549 to 1.550

Part (di) · 2 marks

Find the overall percentage decrease after 10 days of 3% daily exponential decay.

  1. 10.97¹⁰ = 0.73742…
  2. 2Decrease = (1 − 0.73742…) × 100 = 26.25…% ≈ 26.3%

Answer26.3 or 26.25 to 26.26

Part (dii) · 3 marks

Find the number of whole days until the radioactive mass halves at 3% daily decrease.

  1. 1Need 0.97ⁿ < 0.5
  2. 20.97²² = 0.5116… (more than 0.5)
  3. 30.97²³ = 0.4963… (less than 0.5)
  4. 423 days

Answer23

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