A young executive is going to purchase a vacation property for investment purposes. She needs to borrow $$84,000\mathrm{.}00$ for $30$ years at $5\mathrm{.}1\%$ compounded monthly, and will make monthly payments of $$456\mathrm{.}08.($Round all answers to $2$ decimal places.$)$

What is the unpaid balance after $9$ months? $

During this time period, how much interest did she pay? $