Joey realizes that he has charged too much on his credit card and has racked up $$5,500$ in debt If he can pay $$175$ each morth and the card charges $15$ percent APR $($compounded monthly$),$ how long will it take him to pay off the debt?

Note: Do not round intermediate calculations and round your final answer to $2$ decimal places.

Answer is complete but not entirely correct.

True lit pary of the debt

$43\mathrm{.}20$~~ months