A construction company agreed to lease payments of $$486\mathrm{.}18$ on construction equipment to be made at the end of every three months for $3\mathrm{.}5$ years. Financing is at $5\%$ compounded quarterly

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

$($b$)$ If$,$ due to delays, the first $7$ payments were deferred, how much money would be needed after $8$ payments to bring the lease payments up to date?

$($c$)$ How much money would be required to pay off the lease after $8$ payments?

$($d$)$ If the lease were paid off after $8$ payments, what would the total interest be$?$

$($e$)$ How much of the total interest would be due to deferring the first $7$ payments?