Repeated percentage change – GCSE Maths

Foundation and Higher · Grade 6 · Calculator

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Two percentage changes in a row are two multipliers multiplied, not two percentages added. Up $10\%$ then down $10\%$ is $\times 1.1\times 0.9=\times 0.99$, a $1\%$ net loss — not back to the start. Compound growth for $n$ years is original $\times (1+r{)}^n$. A different rate in year 2 is a different multiplier in that year only.

Reverse a two-step change by dividing by both multipliers (in either order). A 'which is better' comparison computes both final amounts with full multipliers, then subtracts. Round to the nearest penny at the end, not after year 1.

Chain the same multiplier: $(1.05{)}^n$. A 10% drop then a 10% rise does not return you to the start ($0.9\times 1.1=0.99$). The single multiplier for five 6% increases is $1.06^5$, not $1.30$.

Objectives

• Increase an amount by the same percent for two years.
• Decrease an amount by the same percent for two years.
• Use the multiplier on its own, and run a change for three years.

Key points

• Turn a percentage change into a multiplier: increase of 3% → 1.03; decrease of 12% → 0.88.
• Apply the same change $n$ times using $(\text{multiplier}{)}^n$.
• Tell the difference between compound interest (on the new total) and simple interest (on the original each year).
• Work backwards to find an original amount or the number of years.

Worked examples

Questions and answers

GCSE Maths repeated percentage change questions and answers. Try each one, then open the answer. Easy questions come first.

Common mistakes

Most lost marks on this topic are one slip.

1. Adding the same percent of the original amount every year

   Multiply by the multiplier once each year

2. Using 0.1 as the multiplier for a 10% increase

   A 10% increase multiplies by 1.1

3. Stopping a three-year change after two years

   Count the years in the question

Exam tips

• A calculator is useful here. Show the calculation you typed, not only the final line.
• If the question says “show that”, the result is given. The marks are for the steps that reach it.
• The method is the same on AQA-style and Edexcel-style papers.
• Write the calculation as one line, e.g. $2000\times 1.03^4$; this line alone usually earns a method mark.
• For 'how many years until…' questions, use the year-by-year method and show the value at each year so the marker can see where it passes the target.

Printable worksheet

The same questions are in a PDF you can print. Answers start on a later page.

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Questions students ask

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More on Repeated percentage change

• Repeated percentage change worked examples and method
  The method in order, key facts and the full lesson explanation
• Repeated percentage change practice questions
  A second set of questions with answers, plus quick checks

AQA-style and Edexcel-style questions. Yumio is not affiliated with, endorsed by or connected to AQA, Pearson Edexcel or any other exam board.

Last updated 9 November 2026.