Use a multiplier for each percentage change, work year by year with and without a calculator, compare savings accounts and growing or shrinking populations, and (Higher) go backwards or take money out each year.
What you will learn
- Write the multiplier for a percentage increase or decrease
- Work out compound interest, growth and decay year by year or with a power
- Turn a year-on-year ratio into a percentage change
- Find when one growing quantity passes another
- Reverse repeated change, and iterate when money is taken out each year (Higher)
One multiplier for each change
A percentage change is a multiplication.
A rise of 4% multiplies by 1.04; a fall of 4% multiplies by 0.96. Repeat it n times and you multiply by the multiplier to the power n. For a fall of 2.5%, take it from 100%: 97.5% = 0.975 (not 0.75, and not 0.025, which is only the part lost).
- £5000 at 3% compound interest for 4 years
- multiplier = 1.03
- 5000 × 1.03⁴ = 5627.544...
- £5627.54
Changes do not add. A rise of 10% then a fall of 10% gives 1.1 × 0.9 = 0.99, a 1% fall overall, not 0%.
When the rate changes from year to year, multiply by each year's multiplier in turn. 4% in the first year and then 2% in each of the next two years is × 1.04 × 1.02². To compare two accounts, work out the final amount in each and compare.
To turn an overall multiplier into a percentage change, compare it with 1. A multiplier of 1.12 is a 12% increase; a multiplier of 0.9405 is 1 − 0.9405 = 0.0595, a 5.95% decrease.
The rest of this lesson and its 10 practice questions are locked.
In this lesson
- One multiplier for each change
- Year by year, without a calculator
- Going backwards and iterating (Higher)
- Try it: Repeat a multiplier on the calculator
10 practice questions, marked as you go; about 30 minutes in all.
Key terms
New, Before
In this unit: Ratio, gradients, similarity and growth
More ratio: one quantity as a fraction of another, ratio notation with units, ratios as linear functions, gradients as rates, similar shapes through length, area and volume ratios, and repeated percentage change.
- Fractions, ratio notation and linear functions
- Gradients as rates
- Similar shapes and scale factors
- Repeated proportional change