Step 1 :Given the following information for an automotive loan: Purchase price: $30,400; sales tax: 7.5%; license and title fees: $350; money credited for trade-in (subtracted from price of vehicle before taxes): $13,200; payments: $499.68 for 72 months.
Step 2 :The total cost of the car can be calculated by adding the purchase price, sales tax, and license and title fees, and then subtracting the money credited for trade-in. The sales tax is calculated on the price of the vehicle after subtracting the trade-in value.
Step 3 :First, subtract the trade-in credit from the purchase price: \(30400 - 13200 = 17200\)
Step 4 :Next, calculate the sales tax: \(17200 * 0.075 = 1290\)
Step 5 :Add the sales tax and license and title fees to the price after trade-in: \(17200 + 1290 + 350 = 18840\)
Step 6 :Final Answer: The total cost of the car is \(\boxed{18840}\)