On January $1,$ the home mortgage balance was $$134,000$ for the home owned by Janet Bennett. The interest rate for the loan is $6$ percent.

Assuming that Janet makes the January monthly mortgage payment of $$1608,$ calculate the following:

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