Problem $5-24$ Number of Annuity Payments $($LG$5-9)$

Joey realizes that he has charged too much on his credit card and has racked up $$5,200$ in debt. If he can pay $$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 intermediate calculations and round your final answer to $2$ decimal places.

Answer is complete but not entirely correct.