Calculate percentages, interest and reverse changes
Find percentages and percentage changes, then apply repeated multipliers for simple or compound interest and reverse percentages for Extended.
Use this pathway for Cambridge IGCSE International Mathematics 0607, 2028–2030. Core and Extended objectives are labelled in each lesson; Extended adds requirements beyond Core. Paper 1 and Paper 2 are non-calculator. Papers 3–6 require a graphic display calculator (GDC). These original lessons use self-checked practice; they are not a Cambridge grade, full timed paper or teacher review.
Before you begin
- Check whether your school has entered you for Core or Extended. Core and Extended share most Number ideas, but some notation and methods are Extended only.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is 15% of $240?
What you will learn
- Find a percentage of a quantity and express one amount as a percentage of another
- Calculate increases, decreases and compound interest
- Use reverse percentages and repeated changes for Extended
Percentages describe a fraction of the current whole
To find p% of a quantity, multiply by p/100. To express A as a percentage of B, calculate A ÷ B × 100%. For a percentage increase, multiply by 1 + p/100; for a decrease, multiply by 1 − p/100.
The starting amount is the denominator when finding a percentage change. A deposit, discount, profit or loss can be expressed as either an amount or a percentage, so check what the question requests.
Use multipliers when a change repeats
Simple interest adds the same percentage of the original principal each period. Compound interest applies the rate to the latest balance, so the balance is multiplied repeatedly. The 0607 syllabus does not supply the interest formula; build it from the yearly multiplier.
Extended also includes reverse percentages and repeated percentage change. To reverse a 15% increase, divide by 1.15; subtracting 15% from the new amount does not undo the original increase.
Pause and explain
A price after a 20% increase is $72. What was the original price?
Worked example
A jacket marked at $800 is discounted by 15%. Find its sale price. Then calculate the balance after $800 earns 4% compound interest for 3 years.
Show the worked solution
- The discount multiplier is 1 − 0.15 = 0.85, so the sale price is 800 × 0.85 = $680.
- For compound interest, multiply the balance by 1.04 for each of the three years.
- $800 × 1.04³ = $899.8912, which is $899.89 to the nearest cent.
Answer Sale price $680; compound balance $899.89 after 3 years.
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.
A phone costs $500 and increases in value by 6% in year one, then 6% in year two. Find its value after two years.
Give me a hint
Use the repeated multiplier 1.06 twice; keep the full value until the end.
Compare my reasoning
- After year one: 500 × 1.06 = $530.
- After year two: 530 × 1.06 = $561.80.
- Equivalently, 500 × 1.06² = 561.80.
$561.80.
Look for these in your work
- Increase multiplier used
- Repeated change applied to new balance
- Equivalent power checked
A shop sells an item for $138 after a 15% profit on cost. Find the cost price.
Give me a hint
The selling price is 115% of cost, so divide by 1.15.
Compare my reasoning
- Let the cost be C. Then 1.15C = 138.
- C = 138 ÷ 1.15.
- Check: 120 × 1.15 = 138.
Cost price $120.
Look for these in your work
- Reverse multiplier selected
- Equation solved
- Profit check confirms the result
A savings account pays 3% compound interest each year. A student wants $2 000 after 4 years. How much must they deposit now, to the nearest cent?
Give me a hint
The future balance is the deposit multiplied by 1.03⁴; reverse that multiplier.
Compare my reasoning
- Let the deposit be P. Then P × 1.03⁴ = 2000.
- P = 2000 ÷ 1.03⁴ = 1776.972… .
- Round the deposit to cents only at the end.
Deposit $1,776.97.
Look for these in your work
- Compound multiplier model set up
- Reverse percentage calculated
- Money rounded at the end
Common mistakes
- Applying a percentage to the wrong starting amount
- Using the same added interest each year for compound interest
- Subtracting the percentage rather than reversing the multiplier
- Rounding a balance after every year
What can you explain now?
What multiplier represents a 12% decrease?
Compare with the explanation
0.88
Subtract 0.12 from 1 to get the remaining proportion.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
How do percentage multipliers differ for increase, decrease, compound growth and a reverse percentage?
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.