Question

A $150,000 loan is to be amortized over 7 years, with annual end-of-year payments. Which of these statements is CORRECT?

a. The proportion of cach payment that represents interest as opposed to repayment of principal would be higher If the interest rate were lower
b. The proportion of interest versus principal repayment would be the same for each of the 7 payments.
c. The proportion of each payment that represents interest versus repayment of principal would be higher if the interest rate were higher
d. The annual payments would be larger if the interest rate were lower
e. If the loan were amortized over 10 years rather than 7 years, and if the Interest rate were the same in either case, the first payment would include more dollars of interest under the 7-year amortization plan.

Answer 1

The correct answer to the question is c. The proportion of each payment representing interest versus repayment of principal would be higher if the interest rate were higher, because with a higher interest rate, a greater portion of each payment goes towards interest rather than reducing the principal balance.

Step-by-step explanation:

The student's question is regarding the amortization of a loan and how the proportions of interest and principal change with varying interest rates and loan terms. When amortizing a loan, the percentage of each payment that goes towards interest versus principal changes with each payment because each payment reduces the remaining principal, upon which the interest is calculated.

Correct Statement

c. The proportion of each payment that represents interest versus repayment of principal would be higher if the interest rate were higher. This is because the interest portion of each payment is calculated based on the remaining balance of the loan. If the interest rate is higher, the interest portion of the payment increases, making less money available to pay down the principal.

Incorrect Statements

a. Incorrect, as the interest proportion would be lower with a lower interest rate, not higher. b. Incorrect because the proportion changes over time as the principal reduces. d. Incorrect, the annual payments would be smaller if the interest rate were lower. e. Incorrect, under the 7-year plan, the interest included in the first payment would be less than under a 10-year plan because the more rapid amortization schedule reduces the principle more rapidly.