You had an amazing spring break vacation, but unfortunately ran over budget. However, you just received an offer in the mail to transfer your $$15,000$ balance from your credit card, which charges an APR of $18\mathrm{.}6\%,$ to a new credit card charging a rate of $9\mathrm{.}2\%$ APR. How long will it take you to pay off your balance on the original credit card if you pay $$275$ a month? $($Assume no new charges are made.$)$ If you balance transfer the $$15,000$ to the new card at $9\mathrm{.}2\%$ APR and continue to make $$275$ monthly payments, how long will it now take you to pay off the balance? $($Assume no new charges are made.$)$ If there is a $2\%$ fee charged for balance transfers, how long will it take you to pay off your card balance if you make monthly payments of $$275$ after transferring your balance to the $9\mathrm{.}2\%$ APR card?