melissa deposits $40,000 into an account that pays 2% interest per year, compounded annually. greg deposits…

Explanation:

Step1: Calculate Greg's 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=$40000$, $r = 0.02$, and $t$ varies for each year. For any year $t$, $I_{Greg}=40000\times0.02\times t$.

Step2: Calculate Melissa's 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 $I_{Melissa}=P(1 + r)^t−P$. For $P = 40000$, $r=0.02$, and $t$ varies for each year.

First - year calculations

For Greg: $I_{Greg1}=40000\times0.02\times1=$800$ For Melissa: $A_{Melissa1}=40000\times(1 + 0.02)^1=40000\times1.02=$40800$ $I_{Melissa1}=40800 - 40000=$800$ They earn the same amount.

Second - year calculations

For Greg: $I_{Greg2}=40000\times0.02\times1=$800$ For Melissa: $A_{Melissa2}=40000\times(1 + 0.02)^2=40000\times1.02^2=40000\times1.0404=$41616$ $I_{Melissa2}=41616 - 40800=$816$ Melissa earns more.

Third - year calculations

For Greg: $I_{Greg3}=40000\times0.02\times1=$800$ For Melissa: $A_{Melissa3}=40000\times(1 + 0.02)^3=40000\times1.02^3=40000\times1.061208=$42448.32$ $I_{Melissa3}=42448.32 - 41616=$832.32$ Melissa earns more.

Answer:

Year	Interest Melissa earns	Interest Greg earns	Who earns more interest?
First	$$800$	$$800$	They earn the same amount.
Second	$$816$	$$800$	Melissa earns more.
Third	$$832.32$	$$800$	Melissa earns more.