On January $1,$ the home mortgage balance was $$127,000$ for the home owned by Sam Rivera. The interest rate for the loan is $7\mathrm{.}5\%.$ Assuming that Sam makes the January monthly mortgage payment of $$1524,$ 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 Sam makes this monthly mortgage payment.