Step 1 :First, subtract the trade-in credit from the purchase price: \(30400 - 13200 = 17200\)
Step 2 :Next, calculate the sales tax by multiplying the price after trade-in by the sales tax rate: \(17200 \times 0.075 = 1290\)
Step 3 :Add the sales tax and license and title fees to the price after trade-in: \(17200 + 1290 + 350 = 18840\)
Step 4 :\(\boxed{18840}\) is the total cost of the car.