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

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

• Year 1: $\pounds 4000\times 1.05=\pounds 4200$

  • This has increased by £200

• Year 2: $\pounds 4200\times 1.05=\pounds 4410$

  • This has increased by £210

• Year 3: $\pounds 4410\times 1.05=\pounds 4630.50$

  • This has increased by £220.50

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

$\begin{array}{rcl}100\%-5\%& =& 95\%\\ 95÷100& =& 0.95\end{array}$

STEP 2

Raise the multiplier to the power of 3

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

$0.{95}^3$

STEP 3

Multiply by the population at the start of 2025

$8000\times 0.{95}^3=6859$

6859 voles

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.

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

$\begin{array}{rcl}100\%+7\%& =& 107\%\\ 107÷100& =& 1.07\end{array}$

• 4% increase

$\begin{array}{rcl}100\%+4\%& =& 104\%\\ 104÷100& =& 1.04\end{array}$

Multiply the original number of stamps by both multipliers

$3750\times 1.07\times 1.04=4173$

4173 stamps