$($Annuity payments$)$ Calvin Johnson has a $$4,500$ debt balance on his Visa card that charges $14\mathrm{.}2$ percent APR compounded monthly. In $2009,$ Calvin's minimum monthly payment is $4$ percent of his debt balance, which is $$180.$ How many months $($round up$)$ will it take Calvin Johnson to pay off his credit card if he pays the current minimum payment of $$180$ at the end of each month? In $2010,$ as the result of a federal mandate, the minimum monthly payment on credit cards rose to $5$ percent. If Calvin made monthly payments of $$225$ at the end of each month, how long would it take to pay off his credit card?

a$.$ 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.$)$