$3.$ You work for the Bank of Champaign and specialize in agricultural lending. Farmer Pat is a close friend and wants to buy a farmland parcel in Champaign County for $$18,000/$acre$.$ The farm is $40$ acres. Pat thinks she can put $30\%$ down and would like a $10-$year loan. She will make annual payments at the end of the year when she receives income from her harvest. Based on her credit history you offer her a $5\mathrm{.}5\%$ loan. Pat wants to know how much her payment will be and how much in total interest she will pay over the $10-$year loan.

a$.$ How much is the loan for?

b$.$ What is her annual loan payment?