A young executive is going to purchase a vacation property for investment purposes. She needs to borrow $$126,000\mathrm{.}00$ for $29$ years at $5\mathrm{.}3\%$ compounded monthly, and will make monthly payments of $$709\mathrm{.}60.($Round all answers to $2$ decimal places.$)$

What is the unpaid balance after $11$ months?

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