Suppose that you wish to buy a new home that will cost you $$500,000.$ You must put $$100,000$ down, and will finance the rest at $3\mathrm{.}6\%$ APR, making monthly payments for $30$ years at the end of each month. However, the loan is structured with a balloon payment of $$100,000$ in the last month. How much will your remaining monthly payments be$?$

Answer choices

$1)<1600$

$2)1600-1700$

$3)1700-1800$

$4)1800-1900$

$5)1900-2000$

$6)>2000$