1. **State the problem:** How long does it take for a 2500 investment to double its value at 5% simple interest per year? 2. **Formula for simple interest:** $$A = P(1 + rt)$$ where $A$ is the amount after time $t$, $P$ is the principal, $r$ is the annual interest rate (as a decimal), and $t$ is the time in years. 3. **Set up the equation:** We want the amount to double, so $A = 2P = 2 \times 2500 = 5000$. 4. Substitute values: $$5000 = 2500(1 + 0.05t)$$ 5. Divide both sides by 2500: $$\frac{5000}{2500} = \cancel{\frac{2500}{2500}}(1 + 0.05t) \Rightarrow 2 = 1 + 0.05t$$ 6. Solve for $t$: $$2 - 1 = 0.05t \Rightarrow 1 = 0.05t \Rightarrow t = \frac{1}{0.05} = 20$$ 7. **Answer:** It takes 20 years for the investment to double at 5% simple interest per year.