You have an outstanding student loan with required payments of $450 per month for the next four years. The interest rate on the loan is 9.8% p.a. with monthly compounding. You are considering making an extra payment of $120 today (that is, you will pay an extra $120 that you are not required to pay). The minimum amount of months for you to pay off this loan with the extra payment is? (Round your answer to a whole integer of months, e.g. 5 months instead of 4.9 months). The correct answer is 37. Show full working out and all explanations leading to the correct answer.