A construction company agreed to lease payments of $$474\mathrm{.}63$ on construction equipment to be made at the end of every month for $6$ years. Financing is at $8\%$ compounded monthly.

$($a$)$ What is the value of the original lease contract?

$($b$)$ If$,$ due to delays, the first $8$ payments were deferred, how much money would be needed after $9$ payments to bring the lease payments up to date?

$($c$)$ How much money would be required to pay off the lease after $9$ payments?

$($d$)$ If the lease were paid off after $9$ payments, what would the total interest be$?$

$($e$)$ How much of the total interest would be due to deferring the first $8$ payments?

$($a$)$ The value of the original lease contract is $

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

$($b$)$ The company would have to pay $

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

$($c$)$ The company would need $

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

$($d$)$ The interest would be $

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

$($e$)$ The interest resulting from the deferral is $

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