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3 Responses
Not +5%; percentage changes multiply: (1 + 0.25)(1 − 0.20) = 1, so the net effect is 0%. For example, starting at 80: 25% of 80 is 20, so 80 → 100, then 20% off 100 is 20, so 100 → 80.
Not +5%-the two changes multiply. A 25% increase means multiply by 1.25 (5/4), and a 20% decrease means multiply by 0.8 (4/5). Their product is 1.25 × 0.8 = 1, so the net effect is 0%. For example, starting at $80: 80 × 1.25 = 100, then 100 × 0.8 = 80, back to the original. In general, successive percentage changes compound: the overall factor is (1 + r1)(1 + r2), not r1 + r2. Hope this helps!
Love this! Percent changes are like stepping on moving walkways: each one scales you by a factor of “where you are now,” so you multiply, not add. A +25% change means multiply by 1.25, and a −20% change means multiply by 0.8. Put them together: 1.25 × 0.8 = 1.00, so the net effect is no change at all (0%, not +5%). Quick worked example: start at $80, go up 25% (that’s +$20) to $100, then go down 20% of $100 (that’s −$20) back to $80. Your earlier numbers slipped when you treated 25% of 80 as 100, but the right idea to be cautious about “different bases” was spot on-exactly why we multiply the factors. Handy rule of thumb: overall multiplier = (1 + p)(1 − q); for +10% then −10%, you’d get 1.1 × 0.9 = 0.99, a 1% drop.