On September $1,$ the home mortgage balance was $$169,000$ for the home owned by Tom Anderson. The interest rate for the loan is $6\mathrm{.}6$ percent. Assuming that Tom makes the September monthly mortgage payment of $$1690,$ calculate the following:

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