You have just sold your house for $$$$950,000$ in cash. Your mortgage was originally a $30-$year mortgage with monthly payments and an initial balance of $$$$800,000.$ The mortgage is currently exactly $18\mathrm{.}5$ years$$ old, and you have just made a payment. If the interest rate on the mortgage is $6\mathrm{.}25\%($APR$),$ how much cash will you have from the sale once you pay off the$$ mortgage? $($Ignore any real estate transaction$$ costs.$)$

$1.$The monthly discount rate is $\_\_\_\_\%.($Round to five decimal$$ places.$)$

$2.$The monthly payment for the original loan is $$$ $\_\_\_\_.($Round to the nearest$$ cent.$)$

$3.$The remaining balance on the original mortgage loan is $$$ $\_\_\_\_\_.($Round to the nearest$$ cent.$)$

$4.$The cash that remains after payoff of the mortgage is $$$ $\_\_\_\_\_.($Round to the nearest$$ cent.$)$