$($Annuity payments$)$ Calvin Johnson has a $$6,000$ debt balance on his Visa card that charges $16\mathrm{.}7$ percent APR compounded monthly. In $2009,$ Calvin's minimum monthly payment is $2$ percent of his debt balance, which is $$120.$ How many months $($round up$)$ will it take Calvin Johnson to pay off his credit card if he pays the current minimum payment of $$120$ at the end of each month? In $2010,$ as the result of a federal mandate, the minimum monthly payment on credit cards rose to $3$ percent. If Calvin made monthly payments of $$180$ at the end of each month, how long would it take to pay off his credit card?

a$.$ If Calvin made monthly payments of $$120$ at the end of each month, how long would it take to pay off his credit card?

months $($Round up to the nearest unit.$)$

b$.$ If Calvin made monthly payments of $$180$ at the end of each month, how long would it take to pay off his credit card?

months $($Round up to the nearest unit.$)$