$($Annuity payments$)$ Calvin Johnson has a $$5,500$ debt balance on his Visa card that charges $14\mathrm{.}3$ percent APR compounded monthly. In $2009,$ Calvin's minimum monthly payment is $3$ percent of his debt balance, which is $$165.$ How many months $($round up$)$ will it take Calvin Johnson to pay off his credit card if he pays the current minimum payment of $$165$ at the end of each month? In $2010,$ as the result of a federal mandate, the minimum monthly payment on credit cards rose to $4$ percent. If Calvin made monthly payments of $$220$ at the end of each month, how long would it take to pay off his credit card?

a$.$ If Calvin made monthly payments of $$165$ 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 $$220$ at the end of each month, how long would it take to pay off his credit card? months $($Round up to the nearest unit.$)$