Suppose you take out a $20-$year mortgage for a house that costs $$427,770.$ Assume the following:

The annual interest rate on the mortgage is $4\%.$

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

The annual property tax is $1\mathrm{.}9\%$ of the cost of the house.

The annual homeowner's insurance is $0\mathrm{.}8\%$ of the cost of the house.

The monthly PMI is $$57$

Your other long$-$term debts require payments of $$583$ 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?