A construction company agreed to lease payments of $$$$546\mathrm{.}02$ on construction equipment to be made at the end of every three months for $6$ years. Financing is at $7\%$ compounded quarterly.

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

$($b$)$ If$,$ due to$$ delays, the first $9$ payments were$$ deferred, how much money would be needed after $10$ payments to bring the lease payments up to$$ date?

$($c$)$ How much money would be required to pay off the lease after $10$payments$?$

$($d$)$ If the lease were paid off after $10$payments$,$ what would the total interest$$ be$?$

$($e$)$ How much of the total interest would be due to deferring the first $9$payments$?$

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Part $1$

$($a$)$ The value of the original lease contract is $$$enter your response here.

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

Part $2$

$($b$)$ The company 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.$)$

Part $3$

$($c$)$ The company would need $$$enter your response here.

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

Part $4$

$($d$)$ The interest would be $$$enter your response here.

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

Part $5$

$($e$)$ The interest resulting from the deferral is $$$enter your response here.

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