On March $1,$ the home mortgage balance was $$239,000$ for the home owned by Tom Carter. The interest rate for the loan is $6\mathrm{.}125$ percent. Assuming that Tom makes the March monthly mortgage payment of $$2868,$ calculate the following:

$($a$)$ The amount of interest included in the March 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.