Question

susan deposits $70,000 into an account that pays simple interest at a rate of 6% per year. joe deposits $70,000 into an account that also pays 6% interest per year. but it is compounded annually. find the interest susan and joe earn during each of the first three years. then decide who earns more interest for each year. assume there are no withdrawals and no additional deposits. year interest susan earns (simple interest) interest joe earns (interest compounded annually) who earns more interest? first $□ $□ susan earns more. joe earns more. they earn the same amount. second $□ $□ susan earns more. joe earns more. they earn the same amount. third $□ $□ susan earns more. joe earns more. they earn the same amount.

Explanation:

Step1: Calculate Susan'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 $P=\$70000$, $r = 0.06$, and $t = 1$ for each year.
For year 1: $I_{Susan1}=70000\times0.06\times1 = 4200$.
For year 2: $I_{Susan2}=70000\times0.06\times1 = 4200$.
For year 3: $I_{Susan3}=70000\times0.06\times1 = 4200$.

Step2: Calculate Joe's 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 year 1:
$A_1=70000\times(1 + 0.06)^1=70000\times1.06 = 74200$, $I_{Joe1}=74200 - 70000=4200$.
For year 2:
$A_2=70000\times(1 + 0.06)^2=70000\times1.1236 = 78652$, $I_{Joe2}=78652 - 74200 = 4452$.
For year 3:
$A_3=70000\times(1 + 0.06)^3=70000\times1.191016=83371.12$, $I_{Joe3}=83371.12 - 78652=4719.12$.

Step3: Compare the interests

For year 1: $I_{Susan1}=4200$ and $I_{Joe1}=4200$, so they earn the same amount.
For year 2: $I_{Susan2}=4200$ and $I_{Joe2}=4452$, so Joe earns more.
For year 3: $I_{Susan3}=4200$ and $I_{Joe3}=4719.12$, so Joe earns more.

Answer:

Year	Interest Susan earns (Simple Interest)	Interest Joe earns (Interest compounded annually)	Who earns more interest?
Second	$\$4200$	$\$4452$	Joe earns more.
Third	$\$4200$	$\$4719.12$	Joe earns more.