Final answer:
The difference between 5-year and 10-year loans for $10,000 with the same interest rate lies in the total interest paid: longer loans cost more overall due to additional years of interest accumulation.
Step-by-step explanation:
The difference between taking out a 5-year loan versus a 10-year loan for $10,000 at identical annual interest rates revolves around the total interest paid over the life of the loan and the monthly payment amounts. The correct answer to the student's question is C. Longer loans cost more overall. This is due to the way interest accumulates over time. Although monthly payments are lower with a longer term loan, the additional years of accruing interest result in a higher total amount paid. Conversely, the monthly payments for a shorter loan are higher, but since the money is borrowed for a shorter period, the total interest paid is less. To illustrate this, we can use examples provided for other scenarios. For instance, a $2,000 loan paid off over 15 years can end up costing over $4,000 in interest, signifying that longer terms yield higher interest costs. Similarly, for a $1,000,000 mortgage over 30 years, a borrower will pay more than twice the original loan amount due to interest. Therefore, the longer the loan term, the more interest accumulates, hence a longer loan period such as 10 years compared to 5 years would be more costly in the end.