Consider a home mortgage of $$225,000$ at a fixed APR of $6\%$ for $30$ years.

a$.$ Calculate the monthly payment.

b$.$ Determine the total amount paid over the term of the loan.

c$.$ Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.

a$.$ The monthly payment is $

$($Do not round until the final answer. Then round to the nearest cent as needed.$)$