You are thinking of purchasing a house. The house costs $$700,000.$ You have $$200,000$ in cash that you can use as a down payment on the house, but you need to borrow the rest of the purchase price. The bank is offering a $30-$year mortgage with monthly payments and has an APR of $6\%.$

$(1)$ What will your monthly payment be$?$

$(2)$ How much of the principal is still owed after one year?

$(3)$ How much will you pay in interest during the first year?