Percentage decrease per lesson

Statement

Giacomino has a wealth of $2000$ euros. He takes ten lessons: at each lesson his wealth decreases by a certain fixed percentage. In the end he is left with $1500$ euros. Determine the percentage $p$ charged at each lesson.

Solution

Each lesson multiplies the wealth by $(1-p)$; after $10$ lessons: $2000\,(1-p)^{10}=1500 \iff (1-p)^{10}=\frac{1500}{2000}=0.75.$ Taking the tenth root: $1-p=0.75^{1/10}\approx 0.9716 \Rightarrow p\approx 0.0284=2.84\%.$

$\boxed{p=1-0.75^{1/10}\approx 2.84\%}$