Suppose you take out a $$206,000$ mortgage for $15$ years at $4\mathrm{.}15\%$ interest.

$($a$)$ Find the monthly payment on this mortgage.

$($b$)$ Fill out the first two rows of the amortization schedule below. Round your answers to the nearest dollar.

$\backslash$table$[[$Payment Number,Interest Payment,Principal Payment,Balance of Loan$],[1,$$$,$$$,$$