A credit card currently has an outstanding balance of $$3,000$ in it$.$ The bank charges $2\%$ interest every month, and the cardholder pays the minimum payment of $$50$ per month. Let yn

be the balance after n months.

a$.$ Find the difference equation and solve it$.$

b$.$Find the balance after $2$ years, assuming no additional purchases.

c$.$When will the credit card balance be zero?