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 month and the card charges $15$ percent APR $($compounded monthly$),$ how long will it take him to pay off the debt?

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

Answer is complete but not entirely correct.

$\backslash$table$[[$Time to pay off the debt,$43\mathrm{.}20,$months$]]$