Question

linda deposits $90,000 into an account that pays 4% interest per year, compounded annually. bob deposits $90,000 into an account that also pays 4% per year. but it is simple interest. find the interest linda and bob 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.

Explanation:

Step1: Calculate Linda's first - year interest

The formula for compound interest is $A = P(1 + r)^t$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. For the first - year, $t = 1$, $P=\$90000$, $r = 0.04$. The interest $I$ is $I=P\times r\times t$. So, $I_{Linda1}=90000\times0.04\times1 = 3600$.

Step2: Calculate Bob's first - year interest

The formula for simple interest is $I = Prt$. With $P = 90000$, $r=0.04$, and $t = 1$, we have $I_{Bob1}=90000\times0.04\times1=3600$.

Step3: Calculate Linda's second - year interest

The principal for the second - year for Linda is $P_2=90000 + 3600=93600$. Then $I_{Linda2}=93600\times0.04\times1 = 3744$.

Step4: Calculate Bob's second - year interest

Bob's principal remains $P = 90000$ for simple interest. So, $I_{Bob2}=90000\times0.04\times1 = 3600$.

Step5: Calculate Linda's third - year interest

The principal for the third - year for Linda is $P_3=93600+3744 = 97344$. Then $I_{Linda3}=97344\times0.04\times1=3901.92$.

Step6: Calculate Bob's third - year interest

Bob's principal is still $P = 90000$. So, $I_{Bob3}=90000\times0.04\times1 = 3600$.

Answer:

Year	Interest Linda earns (Interest compounded annually)	Interest Bob earns (Simple interest)	Who earns more interest?
Second	$\$3744$	$\$3600$	Linda earns more.
Third	$\$3901.92$	$\$3600$	Linda earns more.