Kate earns an annual salary of $$86,000$ and rents a condo for $$1,650$ per month. She has a student loan with a monthly payment of $$450.$ She is considering the purchase of a new vehicle and current financing for new vehicles have a market interest rate of $6\mathrm{.}75\%$ for a $5-$year loan. The lender that she is considering using requires a back$-$end ratio of $40\%.$ She has saved $$4,000$ that she would like to put down on the purchase of the vehicle. What is the maximum vehicle cost she can afford?