Why a 20% Rise Followed by a 20% Fall Is Not Zero

Quick answer: Equal percentage increases and decreases usually do not cancel each other because the second percentage applies to a different starting amount.

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Understand the method

Apply each change in sequence. A 20% increase multiplies a value by 1.20. A 20% decrease then multiplies the new value by 0.80. Together, the multipliers are 1.20 × 0.80 = 0.96.

The rule is useful for understanding discounts, price reversals and changing business metrics. Never simply add successive percentage changes unless the question specifically permits an approximation.

Worked example

A price of $100 rises 20% to $120. It then falls 20% of $120, or $24, ending at $96—a 4% decrease from the original.

What people often get wrong

The second 20% is not $20 because its base is $120, not $100.

A practical way to use this

Track the new base after every percentage step.

Frequently asked question

What increase reverses a 20% fall? A 25% rise from the reduced value restores the original amount.

Successive changes compound

Begin with 100. A 20% increase produces 120. A 20% decrease from that new value removes 24, giving 96. The two changes do not cancel because the second percentage uses a different base.

Apply it to your own task

To combine changes, use multipliers: 1.20 × 0.80 = 0.96. The final level is 96% of the starting level, or a net 4% decrease. This method works for a sequence of increases and decreases.