Related to the Apply the Concept: "Interest Rates and Student Loans"$]$ A student looking at the timeline for a student loan shown in the text just before the Apply the Concept feature and makes the following observation:

The text states that the interest rate on the loan is $4\mathrm{.}6\%,$ but this calculation is obviously wrong. Each monthly payment is $$104,$ so the student will be paying back $$10412=$$$1,248$ per year. Therefore, because the principal of the loan is $$10,000,$ the interest rate must be $$1,\frac{248}{\text{\$}}10,000=0\mathrm{.}1248,$ or $12\mathrm{.}48\%.$

Briefly explain whether you agree with the student's reasoning.

A$.$ Agree. As the student states, there is a payment of $$1,248$ per year, so if the loan is for $$10,000,$ that works out to be $12\mathrm{.}48\%.$

B$.$ Disagree. The payments include both principal and interest. Therefore, the $$104$ monthly payments include paying down the principal of the loan as well as paying interest on the principal.

Disagree. The stated rate on the loan is $4\mathrm{.}6\%,$ which means that even though the loan is made with monthly payments, the borrower is still effectively charged only $4\mathrm{.}6\%$ a year.

D$.$ Agree. Even though the stated interest rate is $4\mathrm{.}6\%,$ payments are made monthly, which means it is compounded more times, so the effective rate works out to be $12\mathrm{.}48\%.$