1. **State the problem:** Matteo has $1500 to invest and wants it to grow to $2500 in 5 years using simple interest. We need to find the interest rate $r$ that will achieve this. 2. **Formula for simple interest:** $$A = P(1 + rt)$$ where $A$ is the future value, $P$ is the principal, $r$ is the interest rate per year, and $t$ is the time in years. 3. **Identify known values:** - $P = 1500$ - $A = 2500$ - $t = 5$ 4. **Substitute known values into the formula:** $$2500 = 1500(1 + 5r)$$ 5. **Divide both sides by 1500 to isolate the term with $r$:** $$\frac{2500}{1500} = \cancel{\frac{1500}{1500}}(1 + 5r)$$ $$\frac{2500}{1500} = 1 + 5r$$ 6. **Simplify the fraction:** $$\frac{2500}{1500} = \frac{5}{3} = 1.6667$$ 7. **Solve for $r$:** $$1.6667 = 1 + 5r$$ $$1.6667 - 1 = 5r$$ $$0.6667 = 5r$$ 8. **Divide both sides by 5:** $$\frac{0.6667}{5} = \cancel{\frac{5}{5}}r$$ $$0.1333 = r$$ 9. **Convert to percentage:** $$r = 0.1333 = 13.33\%$$ **Final answer:** Matteo needs an interest rate of approximately **13.33%** per year to grow his investment to $2500 in 5 years using simple interest.