Suppose you take out a $20-$year mortgage for a house that costs $$401,335.$ Assume the following:

The annual interest rate on the mortgage is $5\%.$

The bank requires a minimum down payment of $17\%$ at the time of the loan.

The annual property tax is $1\mathrm{.}5\%$ of the cost of the house.

The annual homeowner's insurance is $1\mathrm{.}1\%$ of the cost of the house.

The monthly PMI is $$85$

Your other long$-$term debts require payments of $$502$ per month.

If you make the minimum down payment, what is the minimum gross monthly salary you must earn in order to satisfy the $28\%$ rule and the $36\%$ rule simultaneously?

Round your answer to the nearest dollar.