$($Annuity number of periods$)$ Alex Karev has taken out a $$220,000$ loan with an annual rate of $9$ percent compounded monthly to pay off hospital bills from his wife Izzy's illness. If the most Alex can afford to pay is $$2,500$ per month, how long will it take to pay off the loan? How long will it take for him to pay off the loan if he can pay $$3,000$ per month? Use five decimal places for the monthly percentage rate in your calculations.