A stock is at $40. It goes up 25%, then down 20%. Where is it?

How to answer

Back at $40. Up 25% → $50 (40 × 1.25), then down 20% off 50 is −$10 → $40. The trick: a 20% drop exactly offsets a 25% gain because they compound off different bases — 1.25 × 0.80 = 1.00. Sequential percent moves multiply, they don't add.

Key idea: Adding +25% and −20% to get +5% and saying $42 — percent moves are multiplicative, not additive.