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Percent and percentage points

A percentage point is the difference between two percentages. A percent is the relative change. If the interest rate goes from 4% to 5%, it has increased by 1 percentage point, but by 25% of the old rate. Two percentage changes in a row are multiplied as growth factors. An increase of 20% followed by a decrease of 20% does not give the original value, because the decrease is calculated from the new and higher amount.

percent=changeold value⋅100\text{percent} = \frac{\text{change}}{\text{old value}}\cdot 100relative change
1.2⋅0.8=0.961.2\cdot 0.8 = 0.9620% up and 20% down

Symbols

pppercent%

Example

First 20% up and then 20% down: 1.2⋅0.8=0.961.2\cdot 0.8 = 0.96. A rate from 4% to 5% increases by 5−44⋅100=25\frac{5 - 4}{4}\cdot 100 = 25%.

Say percentage points when you compare two rates, and percent when you mean the relative change.
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Part of Mathematics 1T: Exponential models.