Your firm has taken out a $$$$451000$ loan with $8\mathrm{.}2\%$ APR$($compounded monthly$)$ for some commercial property. As is common in commercial real$$ estate, the loan is a $5-$year loan based on a $15-$year amortization. This means that your loan payments will be calculated as if you will take $15$ years to pay off the$$ loan, but you actually must do so in $5$ years. To do$$ this, you will make $59$ equal payments based on the $15-$year amortization schedule and then make a final $60$th payment to pay the remaining balance.

a$.$ What will your monthly payments$$ be$?$

b$.$ What will your final payment$$ be$?$

$($Note$$: Be careful not to round any intermediate steps less than six decimal$$ places.$)$