Final answer:
To determine the payoff time for a car loan, an amortization schedule or financial calculator is used. A $20,000 car loan with 6% interest will take longer to pay off with $100 monthly payments compared to $500 payments due to interest accumulation and the need to cover both interest and principal.
Step-by-step explanation:
The question deals with the computation of loan amortization and determining the time required to pay off a car loan with a given annual interest rate, loan amount, and monthly payment. To calculate how long it will take to pay off a $20,000 car loan at a 6% annual interest rate convertible monthly, an amortization schedule or financial calculator is necessary. For monthly payments of $500, the amortization schedule will show that it takes less time than with monthly payments of $100.
In the given example, if you make monthly installment payments of $100 on a $20,000 loan, the loan will take significantly longer to pay off due to the accumulated interest, and there's a possibility that $100 won't cover the interest that accrues each month, leading to negative amortization. It's crucial to calculate a monthly payment that not only covers the interest but also reduces the principal to ensure the loan is eventually paid off.