Phoebe realizes that she has charged too much on her credit card and has racked up $$5,100$ in debt. If she can pay $$200$ each month and the card charges $18$ percent APR $($compounded monthly$),$ how long will it take her to pay off the debt? $($Do not round intermediate calculations and round your final answer to $2$ decimal places.$)$

Time to pay off the debt

months