Final answer:
The monthly payments and total interest for a car loan can be calculated using the PMT loan payment formula, which involves the cost of the car, the down payment, the annual interest rate, and the loan term. The principal amount is reduced by the down payment and the formula is applied to determine the monthly payments and total interest over the loan period.
Step-by-step explanation:
Calculating monthly payments and total interest on a car loan involves applying the PMT loan payment formula. In this scenario, the car costs $27,635 with an $8,000 down payment. The balance to finance is $27,635 - $8,000 = $19,635. The loan has an annual interest rate of 6.54%, with payments made over five years (or 60 months). The interest rate per month is 6.54% divided by 12. To calculate the monthly payment using the formula PMT = P(n/r) / [1 - (1+n/r)-nt], where P is the principal, n the number of times that interest is compounded per year, t is the time the money is invested or borrowed for, in years, and r is the annual interest rate. We get PMT = $19,635 * (0.0654/12) / [1 - (1 + 0.0654/12)-(12*5)] = $19,635 * 0.00545 / [1 - (1 + 0.00545)-60].
Ultimately, we solve for the monthly payment, which will yield the dollar amount (rounded to the nearest cent), and then multiply this by 60 to find the total amount paid over the life of the loan. Subtracting the initial borrowed amount from this sum gives the total interest paid.