Repeated Percentage Change (Edexcel IGCSE Maths)

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
  • 10 000$\times$1.1³ = 10 000$\times$1.1$\times$1.1$\times$1.1 = 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* *

$8000\times0.95^{3}=6859$

Final answer: 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
  • 10 000$\times$0.86$\times$0.91 = 7826

Exam Hint 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 1.034$\times$0.966

$250000\times1.034\times0.966=249711$

Final answer: $249 711