Kimiko signed a mortgage requiring payments of $$$$310\mathrm{.}32$ at the end of every month for $3$ years at $6\mathrm{.}5\%$ compounded monthly.

$($a$)$ How much was the original mortgage$$ balance?

$($b$)$ If Kimiko missed the first $9$payments$,$ how much would she have to pay after $10$ months to bring the mortgage payments up to$$ date?

$($c$)$ How much would Kimiko have to pay after $10$ months to pay off the mortgage$($assuming she missed all the$$ payments$)?$

$($d$)$ If the mortgage were paid off after $10$months$,$ what would the total interest cost$$ be$?$

$($e$)$ How much of the total interest cost is additional interest because of the missed$$ payments?