Congratulations your $$500,000$ house loan has been approved! Batrez Bank has given you the $30$ year$4\mathrm{.}00\%$ compounded monthly interest rate loan.

It's been exactly $57$ months after you bought the house.You decide to pay an additional $$800$ per month starting this month to try to pay off quicker.

What is the balance before you make the ${57}^{th}$ payment?

How many months would it take to pay off the loan at the new rate?