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Repeated Percentage Change (Edexcel IGCSE Maths B): Revision Note

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Roger B

Written by: Roger B

Reviewed by: Jamie Wood

Updated on

Repeated percentage change

What is repeated percentage change?

  • Repeated percentage change is when several percentage increases or decreases are applied to a quantity, one after the other

How do I calculate repeated percentage change with a constant percentage?

  • Find the percentage multiplier for the increase or decrease

    • If the number of times the percentage change occurs is n

    • Then multiply the original quantity by the percentage multiplier raised to the power of n

  • For example, to increase 10 000 by 10% three times in a row

    • The multiplier is 1.1

    • 10 000cross times1.13 = 10 000cross times1.1cross times1.1cross times1.1 = 13 310

  • Note that this is different to adding 10% to 10 000 three times

    • 10% of 10 000 is 1000

      • 10 000 + 1000 + 1000 + 1000 = 13 000

    • That is the same as increasing 10 000 one time by 30%

Worked Example

The population of voles in a nature reserve is 8000 at the start of 2025.

Due to a new road being built across the reserve, the population is expected to fall by 5% each year.

Calculate the total population of voles expected to be in the nature reserve at the start of 2028.

Answer:

The multiplier for a 5% decrease is 0.95

This occurs three times in a row (three years from start of 2025 to start of 2028)

So multiply 8000 by 0.953

8000 cross times 0.95 cubed equals 6859

6859 voles

How do I calculate repeated percentage change with different percentages?

  • Find the percentage multiplier for each increase or decrease

    • Then multiply the original quantity by those multipliers one after the other

  • For example, to decrease 10 000 by 14% and then by 9%

    • The multipliers are 0.86 and 0.91

    • 10 000cross times0.86cross times0.91 = 7826

Examiner Tips and Tricks

An exam question may combine percentage increases and decreases.

Be sure to use the correct multiplier for each one!

Worked Example

In 2020 Walcher had investments worth $250 000.

From 2020 to 2022, the value of his investments increased by 3.4%.

From 2022 to 2024 the value of his investments decreased by 3.4%.

Calculate the value of Walcher's investments in 2024.

Answer:

Be careful here

  • Increasing an amount by a percentage, and then decreasing the new amount by the same percentage, does NOT get you back to the original amount!

The percentage multipliers are

  • 1.034 for an increase of 3.4%

  • 0.966 for a decrease of 3.4%

These increase and decrease occur one after the other, so multiply 250 000 by 1.034cross times0.966

250000 cross times 1.034 cross times 0.966 equals 249711

$249 711

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Author
Reviewer
Roger B

Author: Roger B

Expertise: Maths Content Creator

Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.

Jamie Wood

Reviewer: Jamie Wood

Expertise: Maths Content Creator

Jamie graduated in 2014 from the University of Bristol with a degree in Electronic and Communications Engineering. He has worked as a teacher for 8 years, in secondary schools and in further education; teaching GCSE and A Level. He is passionate about helping students fulfil their potential through easy-to-use resources and high-quality questions and solutions.