melissa deposits $30,000 into an account that...

# Explanation: ## Step1: Calculate simple - interest formula The simple - interest formula is $I = Prt$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. Given $P=\$30000$, $r = 0.02$. For any year $t$, Greg's simple interest $I_G=30000\times0.02\times t$. ## Step2: Calculate compound - interest formula The compound - interest formula is $A = P(1 + r)^t$, where $A$ is the amount of money in the account after $t$ years, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. The interest earned $I_M=P(1 + r)^t−P$. For $P = 30000$, $r=0.02$. ### First - year calculations #### Greg's interest $I_G=30000\times0.02\times1 = 600$ #### Melissa's interest $A = 30000\times(1 + 0.02)^1=30000\times1.02 = 30600$, $I_M=30600 - 30000=600$ They earn the same amount. ### Second - year calculations #### Greg's interest $I_G=30000\times0.02\times1 = 600$ #### Melissa's interest $A = 30000\times(1 + 0.02)^2=30000\times1.02^2=30000\times1.0404 = 31212$, $I_M=31212 - 30600 = 612$ Melissa earns more. ### Third - year calculations #### Greg's interest $I_G=30000\times0.02\times1 = 600$ #### Melissa's interest $A = 30000\times(1 + 0.02)^3=30000\times1.02^3=30000\times1.061208 = 31836.24$, $I_M=31836.24 - 31212=624.24$ Melissa earns more. # Answer: | Year | Interest Melissa earns (Interest compounded annually) | Interest Greg earns (Simple interest) | Who earns more interest? | | ---- | ---- | ---- | ---- | | First | $\$600$ | $\$600$ | They earn the same amount. | | Second | $\$612$ | $\$600$ | Melissa earns more. | | Third | $\$624.24$ | $\$600$ | Melissa earns more. |