Lisa plans to purchase a new work truck. The dealer requires a $20\%$ down payment on the $$32,000$ vehicle. Lisa will finance the rest of the cost with a fixed$-$rate amortized auto loan at $7\mathrm{.}5\%$ annual interest with monthly payments over $6$ years.

Complete the parts below. Do not round any intermediate computations. Round your final answers to the nearest cent if necessary. If necessary, refer to the list of financial formulas.

$($a$)$ Find the required down payment.

$prod

$($b$)$ Find the amount of the auto loan.

$$$

$($c$)$ Find the monthly payment.