Consider the following pair of loan options for a $$190,000$ mortgage. Calculate the monthly payment and total closing costs for each option. Explain which is the better option and why.

Choice $1$: $20-$year fixed rate at $4\mathrm{.}5\%$ with closing costs of $$1800$ and $1$ point.

Choice $2$: $20-$year fixed rate at $4\mathrm{.}25\%$ with closing costs of $$1800$ and $2$ points.

What is the monthly payment for choice $1?$

$

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