Suppose that you borrow $\$ 16,000$ for three years at $6 \%$ toward the purchase of a car. Use PMT $=\frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]}$ to find the monthly payments and the total interest for the loan. The monthly payment is $\$ \square$. (Do not round until the final answer. Then round to the nearest cent as needed.) The total interest for the loan is $\$$ (Use the answer from part (a) to find this answer. Round to the nearest cent as needed.)

Step 1 ：Given that the principal amount of the loan (P) is $16,000, the annual interest rate (r) is 6% or 0.06, the number of times that interest is compounded per year (n) is 12 (since we are looking for monthly payments), and the time the money is borrowed for in years (t) is 3.

Step 2 ：We can use the formula for the monthly payment (PMT) of a loan, which is \(PMT =\frac{P\left(\frac{r}{n}\right)}{\left[1-\left(1+\frac{r}{n}\right)^{-n t}\right]}\).

Step 3 ：Substitute the given values into the formula to find the monthly payment: \(PMT =\frac{16000\left(\frac{0.06}{12}\right)}{\left[1-\left(1+\frac{0.06}{12}\right)^{-12 \times 3}\right]}\).

Step 4 ：The monthly payment is approximately $486.75.

Step 5 ：To find the total interest paid over the life of the loan, multiply the monthly payment by the total number of payments (n*t), and then subtract the original loan amount (P): \(total\_interest = PMT \times n \times t - P\).

Step 6 ：Substitute the values into the formula to find the total interest: \(total\_interest = 486.75 \times 12 \times 3 - 16000\).

Step 7 ：The total interest for the loan is approximately $1523.04.

Step 8 ：Final Answer: The monthly payment is \(\boxed{\$486.75}\) and the total interest for the loan is \(\boxed{\$1523.04}\).