$(12$ points$)$You finance a used car for $$12,000.$ The credit union gives you a loan with $3\mathrm{.}6\%$ interest rate compounded quarterly for $2$ years. Fill in the following chart with the correct information.

a$.$ Find the payment

b$.$ Fill in the amortization schedule below:

$\backslash$table$[[$Payment$,$Amt Paid,Interest,Principal,Balance$],[0,,,,12,000],[1,,,,],[2,,,,],[3,,,,],[4,,,,],[5,,,,],[6,,,,],[7,,,,],[8,,,,]]$