Step {{ currentStep }} of 4

The Percent Illusion

A 50% increase followed by a 50% decrease doesn't bring you back to where you started.

tune Adjust the sliders

Goal: Set Change 1 to +50% and Change 2 to -50%.

${{ s1_start }}
START
arrow_forward
${{ s1_mid }}
arrow_forward
${{ s1_final }}
FINAL
{{ s1_slider1 > 0 ? '+' : '' }}{{ s1_slider1 }}%
{{ s1_slider2 > 0 ? '+' : '' }}{{ s1_slider2 }}%

Notice how we ended up at $75, not $100!

The 50% decrease was applied to $150, which is a $75 drop.

Trace the Path

Calculate step-by-step. What is the value after each change?

touch_app Tap the answers
Start with ${{ s2_start }}.
First, apply a {{ s2_p1 > 0 ? '+' : '' }}{{ s2_p1 }}% change.
Then, apply a {{ s2_p2 > 0 ? '+' : '' }}{{ s2_p2 }}% change.
${{ s2_start }}
START
{{ s2_p1 > 0 ? '+' : '' }}{{ s2_p1 }}% arrow_forward
{{ s2_mid_selected ? '$' + s2_mid_selected : '?' }}
STEP 1
{{ s2_p2 > 0 ? '+' : '' }}{{ s2_p2 }}% arrow_forward
{{ s2_final_selected ? '$' + s2_final_selected : '?' }}
FINAL

Build the Formula

Convert percent changes into decimal multipliers.

drag_indicator Drag to build
A population of {{ s3_start }} undergoes a {{ Math.abs(s3_p1) }}% {{ s3_p1 > 0 ? 'increase' : 'decrease' }}, followed by a {{ Math.abs(s3_p2) }}% {{ s3_p2 > 0 ? 'increase' : 'decrease' }}.
{{ s3_start }}
close
Multiplier 1
close
Multiplier 2
=
{{ s3_drop1 && s3_drop2 ? s3_final : '?' }}

The Equivalent Single Change

What single percentage change gives the same final result?

unfold_more Adjust the counter
A {{ s4_p1 > 0 ? '+' : '' }}{{ s4_p1 }}% change
followed by a {{ s4_p2 > 0 ? '+' : '' }}{{ s4_p2 }}% change
is equivalent to a single change of...
{{ s4_counter > 0 ? '+' : '' }}{{ s4_counter }}%
Correct! {{ s4_m1 }} × {{ s4_m2 }} = {{ s4_m_final }} ({{ s4_counter > 0 ? '+' : '' }}{{ s4_counter }}%)
workspace_premium

Mastered!

You now understand that compound percents build on each other. Always multiply the multipliers!