Your have just sold your house for $$1,000,000$ in cash. Your mortgage was originally a $30-$year mortgage with monthly payments and an initial balance of $$800,000.$ The mortgage is currently exactly $18\mathrm{.}50$ years old, and you have just made a payment. If the interest rate on the mortgage is $5\mathrm{.}25\%($APR$),$ how much cash will you have from the sale once you pay off the mortgage? $($Ignore any real estate transaction costs.$)$

The discount rate is $\%$ per month. $($Round to five decimal places.$)$

The monthly mortgage payment is $$.($Round to the nearest cent.$)$

The remaining balance is $$.($Round to the nearest dollar.$)$

The cash that remains after payoff of the mortgage is $$.($Round to the nearest dollar.$)$