A used car dealer advertises financing at $0\%$ interest over $3$ years with monthly payments. You must pay a processing fee of $$500$ at signing. The car you like costs $$9000.$

a$)$ What is your effective annual interest rate?

b$)$ You believe that the dealer would accept $$8200$ if you paid cash. What effective annual interest rate would you be paying, if you financed with the dealer?