Percentages

A percentage is a fraction with a denominator of 100.

20 %  =  20/100  =  0,2

That’s all there is to it. Once you’ve got this equivalence in mind, all percentage calculations become simple multiplications.

Calculating a percentage

20 % de 45  =  0,2 x 45  =  9

Increasing and decreasing

To increase by 20 per cent, multiply by 1,2. To decrease by 20 per cent, multiply by 0,8.

50 augmente de 20 %  :  50 x 1,2  =  60
50 diminue de 20 %   :  50 x 0,8  =  40

This coefficient is called the multiplier. It saves you from having to calculate the increase and then add it on — in a single operation, you get the result.

The pitfall: percentages do not add up

A 10 per cent increase followed by a 10 per cent decrease does not bring you back to the starting point:

100  ->  x 1,1  ->  110  ->  x 0,9  ->  99

It’s 1 short. The reason: the 10 per cent decrease is calculated on 110, not on 100. A percentage always relates to a reference value — and this reference has changed between the two stages.

This is exactly why a share that loses 50 per cent must then gain 100 per cent to return to its initial price.