On November $1,$ the home mortgage balance was $$270,000$ for the home owned by Scott Morris. The interest rate for the loan is $9$ percent.

Assuming that Scott makes the November monthly mortgage payment of $$2700,$ calculate the following:

$($a$)$ The amount of interest included in the November payment $($round your answer to the nearest cent$).$

$($b$)$ The amount of the monthly mortgage payment that will be used to reduce the principal balance.

$($c$)$ The new balance after Scott makes this monthly mortgage payment.