Down 25%, then up 25%, the exact damage

Question

A stock falls 25\%, then rises 25\%. Solve in your head. What is the exact net change? Aim: under 10 seconds.

Accepted Answer

The multipliers are (1 - x)(1 + x) = 1 - x^2 with x = 0.25: 0.75 	imes 1.25 = 1 - 0.25^2 = 1 - 0.0625 = 0.9375, a net loss of exactly 6.25\%. Reversing the order changes nothing: multiplication commutes. Takeaway. A \pm 25\% round trip loses 0.25^2 = 6.25\%, whichever leg comes first. Symmetric percentage moves never fully undo each other; the shortfall is always the square of the swing.

Down 25%, then up 25%, the exact damage

Your answer

More Mental Math questions