A washer$-$dryer combination can be purchased from a department store by making monthly credit card payments of $$43\mathrm{.}02$ for three$-$and$-$a$-$half years. The first payment is due on the date of sale and interest is $15\%$ 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?