All courses › Mathematics 1P › Several changes in a row

Several changes in a row

When the price changes several times, you multiply the growth factors. You do not add the percentages, and you do not subtract them from each other. Ten percent up and then ten percent down does not give the original price, because the second change is calculated from the new amount. A growth factor below 1 means the final value is lower than the start. How many percent lower is found by subtracting the growth factor from 1.

Symbols

Example

+10% and then −10%: $1.1 \cdot 0.9 = 0.99$, which is $(1 - 0.99) \cdot 100 = 1$% below the start.

+20% and then −20%: $1.2 \cdot 0.8 = 0.96$, which is 4% below.

← Percent and discount · Backwards and percentage points →

Part of Mathematics 1P: Percentages and growth factors.