Arya borrowed $$400,000$ using a $38-$year, partially amortizing, constant payment mortgage with interest rate of $9\%$ p$.$a$.$ compounded monthly.

The balloon payment due at maturity equals $$100,000.$

The lender charges a loan origination fee of $$12000,$ but agrees to finance the fee.

The monthly payment for Arya equals $ $\_\_\_\_\_\_\_$