$($Nonannual compounding using a calculator$)$ Dennis Rodman has a $$4,500$ debt balance on his Visa card that charges an APR of $12\mathrm{.}3$ percent compounded monthly. Dennis's current minimum monthly payment is $5$ percent of his debt balance, $$225.$ How many months $($round up$)$ will it take Dennis to pay off his credit card if he pays the current miminum payment of $$225$ at the end of each month?

How many months will it take Dennis to pay off his credit card?

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