Suppose you take out a $20-$year mortgage for a house that costs $$404,144.$ Assume the following:

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

$-$ The bank requires a minimum down payment of $12\%$ at the time of the loan.

$-$ The annual property tax is $2\mathrm{.}1\%$ of the cost of the house.

$-$ The annual homeowner's insurance is $0\mathrm{.}6\%$ of the cost of the house.

$-$ Your other long$-$term debts require payments of $$630$ 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.