Lemmara logoLemmaraWorked solution

0580/41 May/Jun 2022, Question 2: Compound Interest

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 13 marks

اقرأ هذا الحل مشروحاً بالعربي ←

The question, in short

Work through ratio sharing, percentage sale prices, compound interest over two years, and exponential decay problems, finding totals, prices, rates, masses and days.

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

Part (a) · 2 marks

Given ratio 3:2:2 and Chris gets 12 strawberries, find the total number shared.

  1. 1Chris's 2 parts = 12, so 1 part = 12 ÷ 2 = 6
  2. 2Total = (3 + 2 + 2) × 6 = 42

Answer42

Part (bi) · 2 marks

Book originally $6.50, reduced by 12%; calculate the amount Dina pays.

  1. 1Multiplier = 1 − 0.12 = 0.88
  2. 26.50 × 0.88 = $5.72

Answer5.72

Part (bii) · 2 marks

Elu pays $11 after a 12% reduction; find the original price of the toy.

  1. 1Original price × 0.88 = 11
  2. 2Original price = 11 ÷ 0.88 = $12.50

Answer12.50

Part (c) · 2 marks

First year interest 2.5%, overall two-year increase 6.6%; find the second year rate.

  1. 11.025 × multiplier = 1.066
  2. 2Multiplier = 1.066 ÷ 1.025 = 1.04
  3. 3Rate for the second year = 4%

Answer4

Part (di) · 2 marks

Substance starts at 80 g, decays 2% per day; find mass after 5 days.

  1. 1Mass = 80 × (1 − 2/100)⁵ = 80 × 0.98⁵
  2. 2= 72.31… ≈ 72.3 g

Answer72.3 or 72.31...

Part (dii) · 3 marks

After day 5, find how many more whole days until mass falls below 67 g.

  1. 180 × 0.98⁸ = 68.06… g (more than 67)
  2. 280 × 0.98⁹ = 66.69… g (less than 67)
  3. 3Mass first below 67 g at the end of day 9
  4. 4Extra days after day 5 = 9 − 5 = 4

Answer4

Stuck on a step? Read the free lesson: Compound Interest

Practise more compound interest questions

Real 0580 past-paper questions, marked on your working like the exam, with a worked solution for every part.

Practise free on Lemmara

More past-paper questions on compound interest

Also searched as: 0580/41/M/J/22 · 0580_s22_qp_41 · 0580 s22 41 · question 2.
Lemmara is an independent study tool, not affiliated with or endorsed by Cambridge International Education. The worked solutions are Lemmara’s own.