Final answer:
To calculate the total interest Michelle pays, first determine the monthly interest rate, then compute the monthly payment using the loan's principal, monthly interest rate, and number of payments. Multiply the monthly payment by 36 and subtract the principal to find the total interest.
This correct answer is none of the above.
Step-by-step explanation:
The question asks us to calculate the total interest paid over the life of a car loan. Michelle made a 10% down payment on a $31,000 car, which means she paid $3,100 upfront (10% of $31,000) and financed the remaining $27,900. The loan has an annual percentage rate (APR) of 3.5% and is to be paid off in 36 months (3 years).
First, we need to find the monthly interest rate by dividing the APR by 12. So, the monthly interest rate is 3.5% / 12, or approximately 0.2917%. To find the monthly payment, we use the formula for an installment loan, which involves the loan amount, the monthly interest rate, and the number of payments:
Monthly Payment = P * (i(1 + i)^n) / ((1 + i)^n - 1)
where P = principal amount ($27,900), i = monthly interest rate (0.2917%), and n = number of payments (36). After calculating the monthly payment, we multiply it by the number of payments (36) to get the total amount paid over the life of the loan. Subtracting the principal from this amount gives us the total interest paid.
Based on this, we can find the option that correctly reflects the total interest paid by Michelle over the life of the loan.
This correct answer is none of the above.