A$$ washer$-$dryer combination can be purchased from a department store by making monthly credit card payments of $$$$38\mathrm{.}46$ for two$-$and$-$a$-$half years. The first payment is due on the date of sale and interest is $16\%$ 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 $$$$9\mathrm{.}00$ per month is added to cover a service$$ contract, what is the value of the entire contract on the date of$$ sale?