1. **Problem statement:** Curtis wants to buy a trumpet costing 360. He deposits 285 into a savings account with 1% monthly compound interest. We need to find the smallest whole number of months $n$ so that the amount in the account is at least 360. 2. **Formula:** The compound interest formula is: $$ A = P(1 + r)^n $$ where: - $A$ is the amount after $n$ months, - $P = 285$ is the principal, - $r = 0.01$ is the monthly interest rate, - $n$ is the number of months. 3. **Goal:** Find the smallest integer $n$ such that: $$ 285(1.01)^n \geq 360 $$ 4. **Trial and improvement:** We test values of $n$: - For $n=25$: $$ 285 \times 1.01^{25} = 285 \times 1.2824 = 365.88 \geq 360 $$ (enough money) - For $n=24$: $$ 285 \times 1.01^{24} = 285 \times 1.2697 = 361.97 \geq 360 $$ (enough money) - For $n=23$: $$ 285 \times 1.01^{23} = 285 \times 1.2571 = 358.39 < 360 $$ (not enough) 5. **Conclusion:** The smallest whole number of months is $\boxed{24}$ months. Curtis must wait 24 months to have enough money to buy the trumpet.