$.$You have just sold your house for $ $1$ comma $100$ comma $000$ in cash. Your mortgage was originally a $30-$year mortgage with monthly payments and an initial balance of $ $800$ comma $000.$ The mortgage is currently exactly $18\mathrm{.}5$ years$$ old, and you have just made a payment. If the interest rate on the mortgage is $7\mathrm{.}25\%($APR$),$ how much cash will you have from the sale once you pay off the$$ mortgage? $($Note$$: Be careful not to round any intermediate steps less than six decimal$$ places$)$