Final answer:
To compare the monthly payments and total interest of two car loans, we use the amortizing loan formula with the terms and interest rates provided. Loan A has a higher monthly payment and lower total interest due to its shorter term and lower interest rate. Loan B has a lower monthly payment but higher total interest because of its longer term and higher interest rate.
Step-by-step explanation:
To determine the monthly payments and total interest for each loan option, we can use the formula for calculating the monthly payment for an amortizing loan: M = P [i(1 + i)^n] / [(1 + i)^n - 1], where M is the monthly payment, P is the principal amount, i is the monthly interest rate, and n is the number of payments.
Loan A: three-year loan (36 months) at a 5.9% annual interest rate.
To find the monthly interest rate, we divide the annual rate by 12.
i = 5.9% / 12 = 0.004917
Using the formula, we can calculate the monthly payment and then the total interest paid over the life of the loan.
Loan B: five-year loan (60 months) at a 7.2% annual interest rate. Similarly, we calculate the monthly interest rate and use the formula to find the monthly payment and total interest.
Comparing the monthly payments and total interest of the two loans will show that Loan A, with a higher monthly payment, results in lower total interest, while Loan B, with a lower monthly payment, results in higher total interest over the life of the loan. This is generally due to the difference in loan terms and interest rates.