You bought a car for $$54,000.$ The downpayment was $$4,000.$ You have a $6-$year auto loan for the remaining amount at an interest rate of $6\mathrm{.}7\%($with monthly compounding$).$

a$.$ What are your monthly payments? What is the effective rate on the loan?

b$.$ They just made the $15$th payment. What is the outstanding balance on the loan?