Question

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 ​, so the student will be paying back per year.​ Therefore, because the principal of the loan is ​, the interest rate must be . The above student statement​ is: A. incorrect because part of each payment is to principal and to interest.​ Therefore, only a portion of the payment goes to​ interest, so the full amount should not be included when computing the rate of interest paid. B. incorrect because the stated rate on the loan is​ 9% which means that even though the loan is made with monthly​ payments, the borrower is still effectively only charged​ 9% a year. C. correct because even though the stated interest rate is​ 9%, payments are made monthly which means it is compounded more times so the effective rate should work out to​ 15.24% D. correct because as the student​ states, there is a payment of per year that works out to​ 15.24%.

Answer 1

Answer: A. incorrect because part of each payment is to principal and to interest.​ Therefore, only a portion of the payment goes to​ interest, so the full amount should not be included when computing the rate of interest paid.

Explanation:

When paying back a loan, there are two components to the periodic interest payment. The first component is the interest payment. This is the payment to compensate the borrower for loaning out the money and is based on the interest rate and the principal left to be repaid.

The second component goes towards repaying the principal of the loan which in this case is $10,000. When computing the periodic interest rate therefore, the entire amount paid per period should not be used as it would inflate the interest rate.