please show the work for how to solve this problem, not in excel

You have an outstanding student loan with required payments of $550 per month for the next four years. The interest rate on the loan is 9% 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 $550, or $750 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.) The number of months to pay off the loan is (Round to two decimal places.)