select the correct answer. which account has the highest effective annual interest rate? a. account 1…

Explanation:

Step1: Recall the effective - annual - rate (EAR) formula

The formula for the effective - annual - rate is $EAR=(1 + \frac{r}{n})^{n}-1$, where $r$ is the annual interest rate (in decimal form) and $n$ is the number of compounding periods per year.

Step2: Calculate EAR for Account 1

For Account 1, $r = 0.0420$ and $n = 4$ (compounded quarterly). $EAR_1=(1+\frac{0.0420}{4})^{4}-1=(1 + 0.0105)^{4}-1\approx1.0426 - 1=0.0426$ or $4.26%$.

Step3: Calculate EAR for Account 2

For Account 2, $r = 0.0415$ and $n = 12$ (compounded monthly). $EAR_2=(1+\frac{0.0415}{12})^{12}-1\approx1.0423 - 1=0.0423$ or $4.23%$.

Step4: Calculate EAR for Account 3

For Account 3, $r = 0.0410$ and $n = 2$ (compounded semiannually). $EAR_3=(1+\frac{0.0410}{2})^{2}-1=(1 + 0.0205)^{2}-1\approx1.0414 - 1=0.0414$ or $4.14%$.

Step5: Calculate EAR for Account 4

For Account 4, $r = 0.0425$ and $n = 1$ (compounded annually). $EAR_4=(1+\frac{0.0425}{1})^{1}-1=0.0425$ or $4.25%$.

Step6: Compare the EARs

Comparing $EAR_1 = 4.26%$, $EAR_2 = 4.23%$, $EAR_3 = 4.14%$, and $EAR_4 = 4.25%$, we can see that $EAR_1$ is the highest.

Answer:

A. Account 1: Interest is compounded quarterly at an annual rate of 4.20%