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Compound Percentage Change (SQA National 5 Applications of Mathematics): Revision Note

Exam code: X844 75

Dan Finlay

Written by: Dan Finlay

Reviewed by: Roger B

Updated on

SQA Applications of MathematicsSQA Maths

Compound percentage change

What is compound percentage change?

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

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

  • STEP 1
    Find the percentage multiplier for the increase or decrease

    • e.g. the multiplier for a 5% increase is 1.05

  • STEP 2
    Raise the multiplier to the power of the number of changes

    • e.g. if an amount increases by 5% each year for 3 years then use 1.053

  • STEP 3
    Multiply by the original amount

    • e.g. consider £4000 increasing by 5% each year for 3 years

      • £ 4000 cross times 1.05 cubed equals £ 4630.50

Examiner Tips and Tricks

Note that this is different to adding 5% to £4000 three times! The actual amount of the increase changes each year.

  • Year 1: £ 4000 cross times 1.05 equals £ 4200

    • This has increased by £200

  • Year 2: £ 4200 cross times 1.05 equals £ 4410

    • This has increased by £210

  • Year 3: £ 4410 cross times 1.05 equals £ 4630.50

    • This has increased by £220.50

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:

STEP 1

Find the multiplier for a 5% decrease

table row cell 100 percent sign minus 5 percent sign end cell equals cell 95 percent sign end cell row cell 95 divided by 100 end cell equals cell 0.95 end cell end table

STEP 2

Raise the multiplier to the power of 3

  • There are three years from start of 2025 to start of 2028

0.95 cubed

STEP 3

Multiply by the population at the start of 2025

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 a further 9%

    • The multipliers are 0.86 and 0.91

    • 10 000 × 0.86 × 0.91 = 7826

Examiner Tips and Tricks

On Paper 1, you might need to find the value after each percentage change. It might be quicker to find common percentages such as 10% and 5% rather than use multipliers.

Worked Example

A museum has a collection of stamps. At the start of 2023 there were 3750 stamps in the collection.

During 2023 the museum increased the size of the collection by 7%.

During 2024 the number of stamps held at the start of the year was increased by a further 4%.

How many stamps were in the museum's collection at the start of 2025?

Answer:

Find the multipliers

  • 7% increase

table row cell 100 percent sign plus 7 percent sign end cell equals cell 107 percent sign end cell row cell 107 divided by 100 end cell equals cell 1.07 end cell end table

  • 4% increase

table row cell 100 percent sign plus 4 percent sign end cell equals cell 104 percent sign end cell row cell 104 divided by 100 end cell equals cell 1.04 end cell end table

Multiply the original number of stamps by both multipliers

3750 cross times 1.07 cross times 1.04 equals 4173

4173 stamps

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Author
Reviewer
Dan Finlay

Author: Dan Finlay

Expertise: Maths Subject Lead

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.

Roger B

Reviewer: 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.