A student looking at the timeline for a student loan on page 60 of the text makes the following observation: The text states that the interest rate on the loan is 9%, but this calculation is obviously wrong. Each monthly payment is $ 127$127, so the student will be paying back $ 127 times 12 equals $ 1 comma 524$127×12=$1,524 per year. Therefore, because the principal of the loan is $ 10 comma 000$10,000, the interest rate must be

No, I do not agree because the monthly payments are calculated using 9% interest compounded montly, and the student is calculating using simple interest.

Explanation:

The question is missing the last part. Thus, I copy the complete question for fully understanding:

A student looking at the timeline for a student loan on page 60 of the text makes the following observation: The text states that the interest rate on the loan is 9%, but this calculation is obviously wrong. Each monthly payment is  $127×12 = $1,524 per year. Therefore, because the principal of the loan is $10,000, the interest rate must be $1,524/ $10,000 = 0.1524 or 15.24%.

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

Answer

The payments of a loan are calculated using compound interest. The formula to calculate the monthly payments is:

             

Where:

Payment is the monthly paymentL is the amount of the loan (principal)i is the monthly interest rate (the annual interest rate divided by 12)n is the number of months

You can obtain the monthly payment of $127 with a an interest rate of 9%, for a $10,000 loan over 10 years, using previous formula:

         

         

The student then will pay $127 × 12 = $1524 per year, but that cannot be used to calculate the annual interest using a simple ratio, which would be valid only for simple interest.