The Adeeva's gross monthly income is $$5200.$ They have $18$ remaining payments of $$300$ on a new car. They are applying for a $15-$year, $$84,000$ mortgage at $6\mathrm{.}5\%.$ The taxes and insurance on the house are $$360$ per month. The bank will only approve a loan that has a total monthly mortgage payment of principal, interest, property taxes, and homeowners' insurance that is less than or equal to $28\%$ of their adjusted monthly income. Complete parts $($a$)$ through $($c$)$ below.

Click the icon to view the table of monthly payments.

a$)$ Determine $28\%$ of the Adeeva's adjusted monthly income.

$ $($Round to the nearest cent.$)$

b$)$ Determine the Adeeva's total monthly mortgage payment, including principal, interest, taxes, and homeowners' insurance.

$ $($Round to the nearest cent.$)$

c$)$ Do they qualify for this mortgage?

Yes