Rukasha Maths

GCSE maths Beta

Compound growth, depreciation and reverse change · Revision guide

Higher · Ratio · 1 page in the PDF

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Learning objectives

  • Apply repeated percentage changes using multipliers.
  • Reverse a percentage change when its multiplier is non-zero.

Key ideas

Growth and depreciation use these multipliers.

m=1+r100orm=1−r100m=1+\frac r{100}\quad\text{or}\quad m=1-\frac r{100}

For depreciation, the percentage lies from zero to one hundred.

0≤r≤1000\le r\le100

After equal periods, raise the multiplier to the number of periods.

F=PmnF=Pm^n

To reverse the change, divide by the accumulated non-zero multiplier.

P=Fmn,m≠0P=\frac{F}{m^n},\qquad m\ne0

Worked examples

Example 1

An £800 device depreciates by 12% each year. Find its value after two years.

m=1−12100=0.88m=1-\frac{12}{100}=0.88
F=800(0.88)2F=800(0.88)^2
800(0.88)=704,704(0.88)=619.52800(0.88)=704,\qquad704(0.88)=619.52
£619.52\pounds619.52

Example 2

A price is £540 after a 20% increase. Find its original value.

m=1.20,P=5401.20m=1.20,\qquad P=\frac{540}{1.20}
£450\pounds450

Watch out

Apply each change to the current amount. A 100% decrease gives zero and cannot be reversed from the final amount alone.