Josh wants to buy a cabin that costs $$89,000.$ The bank requires a $20\%$ down payment. The rest is financed with a $15-$year, fixed$-$rate mortgage at $5\%$ 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.

$s$

$($b$)$ Find the amount of the mortgage.

s$$

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

$$$