Depreciation of a machine

Statement

A machine worth $25\,000\ \text{€}$ loses $15\%$ of its value each year. How much is it worth after $8$ years?

Solution

Each year the value is multiplied by $1 - 0{.}15 = 0{.}85$: $V(t) = V_0\cdot 0{.}85^{t}$. $V(8) = 25\,000\cdot 0{.}85^{8} = 25\,000\cdot 0{.}272491 \approx \boxed{6812{.}26\ \text{€}}.$