Donald buys a machine from Biden Manufacturer and signs a contract that calls for a down payment of $$18000$ and for the payment of $$800$ at the end of every month for $8$ years. The interest rate is $12\%$ p$.$a$.$ compounded quarterly. If Joe missed the first $15$ payments of $$800,$ what must he pay at the time the $16$th payment is due to discharge his indebtedness completely?

A$.$

$$57857\mathrm{.}61$

B$.$

$$59327\mathrm{.}45$

C$.$

$$53198\mathrm{.}98$

D$.$

$$61277\mathrm{.}36$

E$.$

$$63188\mathrm{.}59$

F$.$

$$51778\mathrm{.}58$

G$.$

$$53811\mathrm{.}67$

H$.$

$$54666\mathrm{.}22$

I.

$$55398\mathrm{.}52$

J$.$

$$55999\mathrm{.}81$

K$.$

$$56110\mathrm{.}39$

L$.$

$$48999\mathrm{.}68$