The Percentage Mistakes Almost Everyone Makes (With Fixes)
Percentages feel like primary-school material, yet they trip up shoppers, investors and journalists daily — because several of their behaviours are genuinely counterintuitive. Here are the traps that cost real money, each with the one-line fix. 01 . Trap 1: down 50%, up 50% ≠ back to normal A $100 stock falls 50% to $50. It then rises 50% — to $75, not $100. Percentage changes are always relative to the current base, and the base shrank. To recover from a 50% loss you need a 100% gain; to recover from an 80% loss, a 400% gain. This asymmetry is the core argument for limiting large losses in investing. 02 . Trap 2: stacked discounts don't add '30% off, plus an extra 20% off' is not 50% off. The second discount applies to the already-reduced price: 0.70 × 0.80 = 0.56, so the real discount is 44%. Retailers know the stacked phrasing sounds bigger. Fix: multiply the remaining fractions, never add the percentages. The same logic applies to repeated growth: two years of 10% inflation is not 20% but 1.10 × 1.10 − 1 = 21%. Small gap at low rates, enormous gap over long periods. 03 . Trap 3: percent vs percentage points If a mortgage rate rises from 4% to 5%, it rose by one percentage point but by 25 percent (1 ÷ 4). Headlines exploit this constantly: 'tax rises 25%!' may mean a shift from 4% to 5%. Fix: when comparing two rates, ask 'points or percent?' before reacting. A related trap: a percentage of a percentage. '40% of members voted, and 60% of voters said yes' means 24% of all members said yes — not 60%. 04 . Trap 4: the reversed base 'A is 25% more than B' does not mean 'B is 25% less than A'. If A = 125 and B = 100, then B is 20% less than A. The direction of comparison defines the base, and the base defines the answer. Fix: always name the base explicitly — 'less than what?' — before computing. Takeaway: Every percentage is relative to a base, and every trap above comes from losing track of which base. Name the base, multiply (never add) sequential changes, and distinguish points from percent.