I have a dilemma: I have no money, but I$\text{'}$d like to take my partner on a romantic date to the neighborhood Applebee's. Specifically, I need $$38\mathrm{.}44$ to make this magical night happen.

I approach my friendly neighborhood loan shark, Dr$.$ Andrew Miller $($no relation to the MIST$2090$ instructor$).$ I let him know of my financial situation and he agrees to lend me the money I need if I can pay him $$3/$month at a "perfectly fair" $28\mathrm{.}99\%$ APR $($with monthly compounding$).$

How many months will it take for me to pay back my loan shark? Round to the nearest month.