Calculate percentage changes, profit and interest
Apply percentage multipliers · Use cost as the base for percentage profit · Separate simple and compound interest
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Percentage conversion
- Powers
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Apply percentage multipliers
- Use cost as the base for percentage profit
- Separate simple and compound interest
The base matters
p% of an amount is p/100 times that amount. An increase uses multiplier 1 + p/100; a decrease uses 1 − p/100. Successive changes multiply their factors. Equal percentage increases and decreases do not generally cancel because their bases differ.
Profit = selling price − cost price; percentage profit on cost is profit/cost × 100%. A percentage of selling price is a different measure, so read the stated base.
Two interest models
Simple interest on principal P at rate r per period for n periods is Prn; the total is P(1+rn). Compound interest reinvests each period: total P(1+r)ⁿ and interest total − P. Express r as a decimal and match periods to the quoted rate.
Both simple and compound interest belong to 0444 Core. Reverse percentages and percentiles are separate Extended lessons; the tasks here calculate forwards from the original amount.
Sources for this lesson
Pause and explain
Is compound interest an Extended-only requirement in 0444?
Worked example
Compare simple and compound totals on 500 at 10% per year for two years.
Show the worked solution
- Simple: 500(1 + 0.1×2) = 600.
- Compound: 500(1.1)² = 605; interest is 105.
Answer Simple total 600; compound total 605.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Increase 80 by 15%, then decrease the result by 15%.
Give me a hint
Apply two multipliers.
Compare my reasoning
- 80 × 1.15 = 92.
- 92 × 0.85 = 78.20.
78.20; the equal percentage changes do not cancel.
Look for these in your work
- Use the changed base
- Multiply factors in order
An item costs 40 and sells for 50. Find profit and percentage profit on cost.
Give me a hint
Profit is the difference; its base is cost.
Compare my reasoning
- Profit = 10.
- 10/40 × 100% = 25%.
Profit 10; profit on cost 25%.
Look for these in your work
- State the base
- Distinguish amount and percentage
A deposit of 1200 earns 5% yearly for three years. Find the simple total and compound total, with no withdrawals or fees.
Give me a hint
Use the same yearly rate but different models.
Compare my reasoning
- Simple total = 1200(1 + 0.05×3) = 1380.
- Compound total = 1200(1.05)³ = 1389.15.
Simple 1380; compound 1389.15.
Look for these in your work
- Match periods and rate
- State the no-fee assumption
Common mistakes
- Percentage profit needs the stated base.
- Do not add interest rates when compounding.
What can you explain now?
Is compound interest an Extended-only requirement in 0444?
Compare with the explanation
No; simple and compound interest are in Core too.
The Core percentage section explicitly includes both models.
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Make it stick
Is compound interest an Extended-only requirement in 0444?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.