You need a loan of $$115,000$ to buy a home. Calculate your monthly payments and total closing costs for each choice below. Briefly discuss how you would decide between the two choices.

Choice $1$: $20-$year fixed rate at $5\%$ with closing costs of $$2600$ and no points.

Choice $2$: $20-$year fixed rate at $4\mathrm{.}5\%$ with closing costs of $$2600$ and $3$ points.

What is the monthly payment for choice $1?$

$

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