Kimiko signed a mortgage requiring payments of $$$$309\mathrm{.}96$ at the end of every month for $5$ years at $7\mathrm{.}3\%$ compounded monthly.

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

$($b$)$ If Kimiko missed the first $7$payments$,$ how much would she have to pay after $8$ months to bring the mortgage payments up to$$ date?

$($c$)$ How much would Kimiko have to pay after $8$ months to pay off the mortgage$($assuming she missed all the$$ payments$)?$

$($d$)$ If the mortgage were paid off after $8$months$,$ what would the total interest cost$$ be$?$

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

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Part $1$

$($a$)$ The original mortgage balance was $$$

$$

$15542\mathrm{.}26.$

$($Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as$$ needed.$)$

Part $2$

$($b$)$ Kimiko would have to pay $$$

$$

enter your response here.

$($Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as$$ needed