Jeff and his partner Angel love to take scenic drives along the coast, and they have their hearts set on a $2023$ TESLA Model S$.$ After looking around $($and turning down at least a few too aggressive car salespeople$),$ they decide they can probably get the car they want for about $$83,000.$ With both of their salaries $($Angel makes more money than Jeff$),$ they are confident that they can afford $$1600$ monthly payments.

They get preapproved for a couple loan options through their local credit union $($and know they probably shouldn$$t do dealer financing$)$:

Option $1$: $5$ year loan with an APR of $8\mathrm{.}2\%$ Option $2$: $3$ year loan with an APR of $5\mathrm{.}4\%$

$(10$ points$)$ Angel knows that they will pay less interest overall by choosing the shorter term loan option, but Jeff warns that their monthly payments might be too high. With no down payment, how much would the monthly payment be for loan option $2?$ Show work or Excel formulas used.