You crashed your car and need a new car. As you cannot afford to buy a new car in cash, you decide to lease a $2023$ honda. The car value is $$38,394.$due to amazing credit because you have been building it for years. You accept a lease deal of a $36-$month payment at $$400$ per month, with a $$2,500$ down payment $($neglecting taxes$).$ After $12$ months you have more money and decide to refinance your lease. You negotiate to an $$850$ per month lease, but you now will only have to pay for a total of $24$ months, including the time you have already driven the car.

$($i$)$ Create a piecewise$-$defined function that accurately represents this data.

$($ii$)$ Graph your function.

$($iii$)$ Calculate your total payment of the car at the end of your $24-$month lease $($excluding taxes$).$