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A $150,000 loan is to be amortized over 6 years, with annual end-of-year payments. Which of these statements is CORRECT?

A. The proportion of interest versus principal repayment would be the same for each of the 7 payments.
B. The annual payments would be larger if the interest rate were lower.
C. If the loan were amortized over 10 years rather than 6 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 6-year amortization plan.
D. The proportion of each payment that represents interest as opposed to repayment of principal would be higher if the interest rate were lower.
E. The proportion of each payment that represents interest versus repayment of principal would be higher if the interest rate were higher.



Answer :

GinnyAnswer
Let's analyze each statement step-by-step to determine the correct ones:

1. The proportion of interest versus principal repayment would be the same for each of the 7 payments.

This statement is incorrect. In an amortizing loan, early payments are composed of a larger proportion of interest, with the interest portion decreasing over time and the principal portion increasing. Therefore, the proportion of interest versus principal repayment is not the same for each payment.

2. The annual payments would be larger if the interest rate were lower.

This statement is incorrect. If the interest rate is lower, the cost of borrowing is reduced, and thus, the annual payments would be smaller, not larger.

3. If the loan were amortized over 10 years rather than 6 years, and if the interest rate were the same in either case, the first payment would include more dollars of interest under the 6-year amortization plan.

This statement is correct. Given the same loan amount and interest rate, a shorter amortization period (6 years) means that each payment must be larger because the loan is being repaid over a shorter period. Consequently, the initial payments will have a higher interest component compared to a longer amortization period (10 years).

4. The proportion of each payment that represents interest as opposed to repayment of principal would be higher if the interest rate were lower.

This statement is incorrect. If the interest rate is lower, a smaller portion of each payment is allocated to interest, meaning a larger portion goes toward the principal. Therefore, the proportion of interest is actually lower with a lower interest rate, not higher.

5. The proportion of each payment that represents interest versus repayment of principal would be higher if the interest rate were higher.

This statement is correct. A higher interest rate results in a larger portion of each payment going towards interest rather than the principal repayment.

Based on the analysis:

- Statement 3 is correct.
- Statement 5 is correct.

Thus, the correct statements regarding the loan amortization are statements 3 and 5.

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