Question $1(10$ points$)$ Today is Max$$s lucky day! They won $$85,000\mathrm{.}00$ on a lottery scratch ticket. Max is excited to pay off a car loan they took out $18$ months ago. The first $$2,000\mathrm{.}00$ payment was due $2$ months ago; however, Max was not able to pay it$.$ Additional payments as per loan agreement are $$2,860\mathrm{.}00$ and $$2,500\mathrm{.}00$ due $3$ and $20$ months from now, respectively. This loan charges interest at $18\mathrm{.}45\%$ compounded semiannually. Max is hoping to pay off the loan with lump sum in $5$ months when they receive the winnings. How much is the payment required to pay off the loan at the focal date?