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3 Responses
Because the second 25% is taken on a bigger number than the first one. Starting at 80, a 25% increase adds 20, taking you to 100. Now when you add “another 25%,” you’re taking 25% of 100, which is 25, not 20. So you end up at 125. That’s an overall jump of 45 from the original 80, which is 45/80 = 56.25%. The two steps “stack” on each other-like climbing two stairs where the second stair is a little taller because you’re already higher up.
In general, percentage changes compound: two successive +25% changes multiply as 1.25 × 1.25 = 1.5625, i.e., a 56.25% overall increase. A single +50% change is just a factor of 1.5, which is slightly smaller. If you wanted two equal bumps to make exactly +50% overall, each bump would need to be about 22.47% since (1 + x)² = 1.5. Hope this helps!
Great question! The trick is that each percentage increase is taken on the current amount, not the original. Starting at 80, a 25% increase gives 80 × 1.25 = 100. Now you’re 25% up on 100, so you do 100 × 1.25 = 125. That’s bigger than a single 50% jump from 80, which would be 80 × 1.5 = 120. In fact, two 25% increases multiply: 1.25 × 1.25 = 1.5625, so the total increase is 56.25%, not 50%. Algebra fans will spot the pattern: (1 + 0.25)(1 + 0.25) = 1 + 0.25 + 0.25 + 0.25×0.25, and that little extra 0.0625 (6.25%) is the “growth on growth.” Tiny analogy: think of rolling a snowball-add 25% more snow, then add 25% of the now-bigger snowball; because the second scoop is larger, you end up with more than just half-again the original.
Because each 25% is applied to the new amount, you multiply factors: 80 × 1.25 × 1.25 = 125 (a 56.25% total increase), whereas a single 50% increase is 80 × 1.5 = 120. Does thinking of successive percentage changes as multiplying by factors make sense here? See: https://www.mathsisfun.com/numbers/percentage-change.html