A construction company agreed to lease payments of $$$$538\mathrm{.}19$ on construction equipment to be made at the end of every three months for $5$ years. Financing is at $7\%$ compounded quarterly.

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

$($b$)$ If$,$ due to$$ delays, the first $10$ payments were$$ deferred, how much money would be needed after $11$ payments to bring the lease payments up to$$ date?

$($c$)$ How much money would be required to pay off the lease after $11$payments$?$

$($d$)$ If the lease were paid off after $11$payments$,$ what would the total interest$$ be$?$

$($e$)$ How much of the total interest would be due to deferring the first $10$payments$?$