You have an outstanding student loan with required payments of $$500$ 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 $$200$ a month in addition to your required monthly

payments of $$500,$ or $$700$ 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.$)$

You can pay off the loan in months. $($Round to two decimal places.$)$