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.$

She always pays on time.

After paying the loan for $120$ months, the balance of this loan equals $ $\_\_\_\_\_\_\_\_.$

Hint: calculate the monthly payment first. Pay attention to the sign of the balloon payment in your calculation.