melanie is looking for a loan. she is willing to pay no more than an effective rate of 9.955% annually…

Explanation:

Step1: Recall effective - rate formula

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

Step2: Calculate EAR for Loan A

For Loan A, $r = 0.09265$ and $n = 52$ (compounded weekly). $EAR_A=(1+\frac{0.09265}{52})^{52}-1\approx(1 + 0.00178173)^{52}-1\approx1.0969 - 1=0.0969 = 9.69%$

Step3: Calculate EAR for Loan B

For Loan B, $r = 0.09442$ and $n = 12$ (compounded monthly). $EAR_B=(1+\frac{0.09442}{12})^{12}-1\approx(1+0.00786833)^{12}-1\approx1.0981 - 1 = 0.0981=9.81%$

Step4: Calculate EAR for Loan C

For Loan C, $r = 0.09719$ and $n = 4$ (compounded quarterly). $EAR_C=(1+\frac{0.09719}{4})^{4}-1\approx(1 + 0.0242975)^{4}-1\approx1.1002-1 = 0.1002=10.02%$

Step5: Compare with Melanie's criteria

Melanie is willing to pay an effective rate of no more than $9.955%$. Loans A ($9.69%$) and B ($9.81%$) meet her criteria, while Loan C ($10.02%$) does not.

Answer:

c. A and B