christine deposits $50,000 into an account that pays simple interest at a rate of 4% per year. kevin…

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=$50000$, $r = 0.04$. For Christine (simple interest): For year 1 ($t = 1$): $I_{1s}=Prt=50000\times0.04\times1=$2000$ For year 2 ($t = 2$): $I_{2s}=Prt=50000\times0.04\times2=$4000$ For year 3 ($t = 3$): $I_{3s}=Prt=50000\times0.04\times3=$6000$

Step2: Calculate compound - interest formula

The compound - interest formula is $A=P(1 + r)^t$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years the money is invested for. The interest earned $I=A - P$. For Kevin (compound interest): For year 1 ($t = 1$): $A_1=P(1 + r)^1=50000\times(1 + 0.04)^1=50000\times1.04=$52000$ $I_{1c}=A_1 - P=52000-50000=$2000$ For year 2 ($t = 2$): $A_2=P(1 + r)^2=50000\times(1 + 0.04)^2=50000\times1.04^2=50000\times1.0816=$54080$ $I_{2c}=A_2 - P=54080 - 50000=$4080$ For year 3 ($t = 3$): $A_3=P(1 + r)^3=50000\times(1 + 0.04)^3=50000\times1.124864=$56243.2$ $I_{3c}=A_3 - P=56243.2-50000=$6243.2$

Answer:

Year	Interest Christine earns (Simple interest)	Interest Kevin earns (Interest compounded annually)	Who earns more interest?
First	$$2000$	$$2000$	They earn the same amount.
Second	$$2000$	$$2080$	Kevin earns more.
Third	$$2000$	$$2163.2$	Kevin earns more.