a newly hired lawyer receives a $15,000 signing bonus from a law firm and invests the money in a savings…

Explanation:

Step1: Identify the formula for compound - interest compounded quarterly

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. Here, $P=$15000$, $r = 0.0475$, $n = 4$ (compounded quarterly), and $t=\frac{42}{12}=3.5$ years.

Step2: Calculate the amount $A$ for quarterly - compounded interest

$A = 15000(1+\frac{0.0475}{4})^{4\times3.5}=15000(1 + 0.011875)^{14}$. First, calculate $(1 + 0.011875)^{14}$. Using a calculator, $(1 + 0.011875)^{14}\approx1.1817$. Then $A=15000\times1.1817=$17725.5$. The interest earned $I_{A}=A - P=17725.5−15000=$2725.5$.

Step3: Identify the formula for continuous - compounding

The formula for continuous - compounding is $A = Pe^{rt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. Here, $P = 15000$, $r=0.0475$, and $t = 3.5$.

Step4: Calculate the amount $A$ for continuous - compounding

$A=15000e^{0.0475\times3.5}=15000e^{0.16625}$. Using a calculator, $e^{0.16625}\approx1.1819$. Then $A = 15000\times1.1819=$17728.5$. The interest earned $I_{B}=A - P=17728.5−15000=$2728.5$.

Step5: Calculate the difference in interest

The difference in interest $\Delta I=I_{B}-I_{A}=2728.5 - 2725.5=$3$.

Answer:

Part A: The interest earned when compounded quarterly is $$2725.5$. Part B: The interest earned when compounded continuously is $$2728.5$. Part C: The difference in the amount of interest earned is $$3$.