karen deposits $20,000 into an account that pays simple interest at a rate of 4% per year. david deposits…

Explanation:

Step1: Calculate Karen'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=$20000$, $r = 0.04$, and for each year $t = 1$. For any year $n$, $I_{Karen}=20000\times0.04\times1 = 800$.

Step2: Calculate David'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 $I = A - P$.

First year:

$A_1=20000(1 + 0.04)^1=20000\times1.04 = 20800$. $I_{David1}=20800 - 20000=800$.

Second year:

$A_2=20000(1 + 0.04)^2=20000\times1.04^2=20000\times1.0816 = 21632$. $I_{David2}=21632 - 20800 = 832$.

Third year:

$A_3=20000(1 + 0.04)^3=20000\times1.04^3=20000\times1.124864 = 22497.28$. $I_{David3}=22497.28 - 21632=865.28$.

Answer:

Year	Interest Karen earns (Simple interest)	Interest David earns (Interest compounded annually)	Who earns more interest?
First	$$800$	$$800$	They earn the same amount.
Second	$$800$	$$832$	David earns more.
Third	$$800$	$$865.28$	David earns more.