On December $1,$ the home mortgage balance was $$319,000$ for the home owned by Kim Parker. The interest rate for the loan is $9$ percent.

Assuming that Kim makes the December monthly mortgage payment of $$2552,$ calculate the following:

$($a$)$ The amount of interest included in the December 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 Kim makes this monthly mortgage payment.