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0580/42 Feb/Mar 2023, Question 1: Simple Interest

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 16 marks

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The question, in short

Multi-part money problem: sharing in ratios, percentages, simple and compound interest, reverse percentage, and finding a rate.

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

Part (ai) · 1 mark

Show that Alain's share of $750, split 8:7 with Beatrice, is $400.

  1. 1Total parts = 8 + 7 = 15
  2. 2One part = 750 ÷ 15 = $50
  3. 3Alain = 750/(8 + 7) × 8 = 50 × 8 = $400

Answer750/(8 + 7) × 8 = 400

Part (aiia) · 1 mark

Express $150 as a percentage of $400.

  1. 1150/400 × 100
  2. 2= 37.5%

Answer37.5

Part (aiib) · 3 marks

Find the total from investing $250 at 2% simple interest for 5 years.

  1. 1Interest = 250 × 2 × 5/100 = $25
  2. 2Amount = 250 + 25 = $275

Answer275

Part (aiii) · 3 marks

Find Beatrice's $350 after 5 years at 0.25% monthly compound interest, to the nearest dollar.

  1. 15 years = 60 months
  2. 2Amount = 350 × (1 + 0.25/100)⁶⁰ = 350 × 1.0025⁶⁰
  3. 3= 406.56…
  4. 4≈ $407

Answer407

Part (b) · 2 marks

Share 100 oranges with Carl:Dina = 3:5 and Carl:Eva = 2:3; find Carl's number.

  1. 1C : D = 3 : 5 = 6 : 10
  2. 2C : E = 2 : 3 = 6 : 9
  3. 3C : D : E = 6 : 10 : 9, total 25 parts
  4. 4Carl = 6/25 × 100 = 24

Answer24

Part (c) · 3 marks

House rises 5% then 3% to $60 564; find the original price Fred paid.

  1. 1Original × 1.05 × 1.03 = 60564
  2. 2Original = 60564 ÷ (1.05 × 1.03) = 60564 ÷ 1.0815
  3. 3= $56000

Answer56000

Part (d) · 3 marks

Find r when $500 grows to $609.20 over 8 years at r% compound interest.

  1. 1500 × (1 + r/100)⁸ = 609.20
  2. 2(1 + r/100)⁸ = 609.20 ÷ 500 = 1.2184
  3. 31 + r/100 = ⁸√1.2184 = 1.024999…
  4. 4r = 2.499… ≈ 2.50

Answer2.50 or 2.499...

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Also searched as: 0580/42/F/M/23 · 0580_m23_qp_42 · 0580 m23 42 · question 1.
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