Jenny plans to buy a used truck that costs $$24,000.$ The dealer requires a $10\%$ down payment. The rest of the cost is financed with a $4-$year, fixed$-$rate amortized auto loan at $4\mathrm{.}5\%$ annual interest with monthly payments.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.$($b$)$ Find the amount of the auto loan.$($c$)$ Find the monthly payment.