You have an outstanding student loan with required payments of $$$$550$ per month for the next $4$ years. The interest rate on the loan is $9\mathrm{.}0\%$ APR$($compounded monthly$).$ Now that you realize your best investment is to prepay your student$$ loan, you decide to prepay as much as you can each month. Looking at your$$ budget, you can afford to pay an extra $$$$175$ a month in addition to your required monthly payments of $$$$550,$ or $$$$725$ in total each month. How long will it take you to pay off the$$ loan? $($Note$$: Be careful not to round any intermediate steps less than six decimal$$ places.$)$