interest is $19\%$ compounded monthly.

$($a$)$ What is the purchase price?

$($b$)$ How much will be paid in installments?

$($c$)$ How much is the cost of financing?

$($d$)$ If an additional $$8\mathrm{.}50$ per month is added to cover a service contract, what is the value of the entire contract on the date of sale?

a$)$ The purchase price is $

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