You have just sold your house for $$900,000$ in cash. Your mortgage was originally a $30-$year mortgage with monthly payments and an initial balance of $$825,000.$ The mortgage is currently exactly

$19\mathrm{.}5$ years old, and you have just made a payment. If the interest rate on the mortgage is $5\mathrm{.}25\%($APR with semi$-$annual compounding$),$ how much cash will you have from the sale once you pay off

the mortgage? $($Note: Be careful not to round any intermediate steps.$)$

a$.$ What is the discount rate for the mortgage?

The discount rate for the mortgage is $,\%.($Round to six decimal places to answer, but carry full precision for remaining calculations.$)$

b$.$ What is the monthly mortgage payment?

The monthly mortgage payment is $$,.($Round to the nearest cent, for example, $1234\mathrm{.}56$ to answer, but carry full precision for remaining calculations.$)$

c$.$ What is the remaining balance on the mortgage?

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

d$.$ How much cash will you have from the sale once you pay off the mortgage?

The amount of cash left over from the sale is $$,.($Round to the nearest cent.$)$