The rule
final = value × (1 + p₁) × (1 + p₂) × (1 + p₃)
Why it works
Each percentage applies to the result of the previous one, not to the original. That is why they multiply rather than add, and why the order in which they are quoted never matches the arithmetic.
How to do it by hand
- Turn each percentage into a factor: +10 % gives 1.1, −10 % gives 0.9
- Multiply the starting value by the first factor
- Multiply that result by the next, and so on
- The real change is the final value against the first
What is worth knowing
The classic demonstration is +10 % then −10 %, which does not return you to the start but leaves you at 99: down 1 %. The loss is always in the same direction, whatever the order, and it grows with the size of the swings — +50 % then −50 % leaves you at 75. This is why volatility hurts investment returns even when the average change is zero, and it is the reason compound annual growth rate exists as a separate concept from the average of the yearly returns.