linda deposits $90,000 into an account that pays 4% interest per year, compounded annually. bob deposits…

Explanation:

Step1: Calculate Bob'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=$90000$, $r = 0.04$, and $t$ varies for each year.

Step2: Calculate Linda's compound - interest formula

The compound - interest formula is $A=P(1 + r)^t$, and the interest earned $I=A - P=P((1 + r)^t-1)$. For $P = 90000$ and $r = 0.04$.

First - year calculations

Bob's interest

$I_{Bob1}=Prt=90000\times0.04\times1 = 3600$.

Linda's interest

$I_{Linda1}=90000\times((1 + 0.04)^1-1)=90000\times(1.04 - 1)=90000\times0.04 = 3600$. They earn the same amount in the first year.

Second - year calculations

Bob's interest

$I_{Bob2}=Prt=90000\times0.04\times1 = 3600$.

Linda's interest

$A_{Linda2}=90000\times(1 + 0.04)^2=90000\times1.0816$, $I_{Linda2}=90000\times1.0816-90000=90000\times(1.0816 - 1)=90000\times0.0816 = 3744$. Linda earns more in the second year.

Third - year calculations

Bob's interest

$I_{Bob3}=Prt=90000\times0.04\times1 = 3600$.

Linda's interest

$A_{Linda3}=90000\times(1 + 0.04)^3=90000\times1.124864$, $I_{Linda3}=90000\times1.124864-90000=90000\times(1.124864 - 1)=90000\times0.124864 = 3901.92$. Linda earns more in the third year.

Answer:

Year	Interest Linda earns (Interest compounded annually)	Interest Bob earns (Simple Interest)	Who earns more interest?
First	$$3600$	$$3600$	They earn the same amount.
Second	$$3744$	$$3600$	Linda earns more.
Third	$$3901.92$	$$3600$	Linda earns more.