Use PMT $=\frac{P(\frac{r}{n})}{[1-(1+\frac{r}{n}{)}^{-nt}]}$ to determine the regular payment amount, rounded to the nearest cent. The cost of a home is financed with a $$160,00020-$year fixed$-$rate mortgage at $4\mathrm{.}5\%.$

a$.$ Find the monthly payments and the total interest for the loan.

b$.$ Prepare a loan amortization schedule for the first three months of the mortgage.

a$.$ The monthly payment is $ $$

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