A young executive is going to purchase a vacation property for investment purposes. She needs to borrow $$127,000\mathrm{.}00$ for $29$ years at $6\mathrm{.}2\%$ compounded monthly, and will make monthly payments of $$787\mathrm{.}15.($Round all answers to $2$ decimal places.$)$

What is the unpaid balance after $10$ months?

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