Mathematics 0580 · syllabus C1.13, E1.13, E1.17
Cambridge IGCSE Mathematics 0580 — Percentages and interest topical past papers
Percentages of amounts, percentage change, profit and loss, simple and compound interest, and on the Extended route reverse percentages and growth and decay.
- Questions
- 478
- Years
- 2009–2026
- With mark scheme
- 93%
- Questions 2022–2026
- 167
Anyone can browse these pages. Opening the questions and their mark schemes takes a free Momentum account.
What Percentages and interest covers
A percentage is a number out of 100. You find a percentage of a quantity, work out what percentage one quantity is of another, and calculate percentage increases and decreases, often with money: a sale discount, a deposit, a pay rise, or the profit or loss on a sale, with answers that can be more than 100%. A multiplier is the quickest method with a calculator: an increase of 15% multiplies by 1.15, and a decrease of 15% by 0.85. A percentage change is the change divided by the original value, times 100.
Simple interest adds the same amount each year, a fixed percentage of the original sum. Compound interest adds each year's interest to the balance, so the amount after n years is P × (1 + r/100)ⁿ; neither formula is given, so you need to know them. Extended adds reverse percentages, where you find the original value from the value after a change by dividing by the multiplier, and repeated percentage change in other settings, known as exponential growth and decay, as with a population rising by 3% a year or a car losing 12% of its value each year.
Percentages and simple and compound interest are Core content, so they can be set on all four papers; reverse percentages and exponential growth and decay are Extended, examined only on Papers 2 and 4. Without a calculator, percentages are built from 10%, 5% and 1%, so 35% of $260 is 3 × $26 + $13 = $91. The topic connects to fractions and decimals, to ratio, and on the Extended route to graphs of exponential growth and decay.
In the syllabus
The headings this topic has in the Cambridge International 2025–2027 syllabus, as the board prints them.
- C1.13 Percentages
- E1.13 Percentages
- E1.17 Exponential growth and decay
What you should be able to do
- Find a percentage of a quantity, with and without a calculator
- Find what percentage one quantity is of another, including answers over 100%
- Calculate percentage increase, decrease, profit and loss using multipliers
- Work out simple and compound interest, and the value of an investment after a number of years
- Find an original value from a value after a percentage change (Extended)
- Model repeated percentage change, such as depreciation or population growth (Extended)
Key ideas
- Percentage change = (change ÷ original value) × 100
- Multiplier for an increase of r%: 1 + r/100; for a decrease of r%: 1 − r/100
- Simple interest = P × r × n ÷ 100; compound amount = P × (1 + r/100)ⁿ
- Reverse percentage: original value = new value ÷ multiplier (Extended)
- Repeated change by the same percentage multiplies by the same factor each time, which is exponential growth or decay (Extended)
How Percentages and interest has been examined
From 2022 to 2026, Percentages and interest was on Paper 3 · Calculator (Core) in 14 of 14 exam series, worth about 16% of that paper’s marks.
| Paper | Questions | Share of marks | Series |
|---|---|---|---|
| Paper 1 · Non-calculator (Core) | 34 | 4% | 14 of 14 |
| Paper 2 · Non-calculator (Extended) | 21 | 3% | 12 of 14 |
| Paper 3 · Calculator (Core) | 62 | 16% | 14 of 14 |
| Paper 4 · Calculator (Extended) | 50 | 11% | 14 of 14 |
Momentum’s own count, over the questions in its bank for these years: a series is one exam session, every zone included, and a question filed under two chapters counts in both. Median marks per question: 4.
Filed in Momentum under: Percentages, Simple and Compound Interest.
A worked example
Mia invests $2500 at 4% per year compound interest. Find the value of her investment after 3 years and the total interest, and compare it with simple interest at the same rate.
- An increase of 4% each year means multiplying by 1.04 each year.
- After 3 years the value is 2500 × 1.04³ = 2500 × 1.124864 = $2812.16.
- Total interest = $2812.16 − $2500 = $312.16.
- Simple interest at 4% would add 4% of $2500, which is $100, each year, so $300 over 3 years.
- Compound interest earns $312.16 − $300 = $12.16 more, because each year's interest earns interest itself.
Answer: $2812.16 after 3 years; $312.16 of interest, $12.16 more than simple interest
Written by Momentum for this page, with its own numbers; it is not taken from a past paper.
Mistakes that cost marks
- Dividing by the new value when finding a percentage change: the change is always compared with the original value.
- Finding a reverse percentage by adding the percentage to the new price: if $68 is the price after a 15% discount, the original is $68 ÷ 0.85 = $80, not $68 plus 15% of $68.
- Using simple interest when the question says compound, or adding the first year's interest n times.
- Giving the interest when the question asks for the total amount, or the reverse: read whether the answer is the interest earned or the value of the account.
- Rounding the balance at the end of each year, which can leave the final amount a few cents out: work out P × (1 + r/100)ⁿ in one calculation and round once, at the end.
Exam technique
- Write the multiplier first, such as 0.88 for a 12% decrease, then use it once for each change.
- For compound interest, show the calculation, such as 2500 × 1.04³, in full, then give money to the nearest cent.
- Check a reverse percentage by applying the percentage change to your answer and getting back the value you were given.
Practising in Momentum
- Every question in a chapter as one list, from every paper and year in the bank, newest first or shuffled.
- Each question turns over to its own part of the mark scheme, where the board published one.
- Narrow by paper, year, session, zone and marks, and star the questions worth keeping.
- Pick chapters, a number of questions and a time, and the exam builder draws a mock to sit and mark.
Past-paper questions and mark schemes are the copyright of Cambridge International. Momentum shows them to signed-in learners for revision and does not publish them on these pages.