We have 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.
The total cost of the car is $\$ 18840$
The amount financed is $\$ 18840$
The total installment price is $\mid \$$

Step 1 ：First, calculate the total cost of the car including sales tax and license and title fees. The total cost is the purchase price minus the trade-in value, plus the sales tax on the reduced price, plus the license and title fees. So, the total cost is \(\$30,400 - \$13,200\) times \(1 + 0.075\) plus \$350, which equals \$18840.

Step 2 ：Next, calculate the amount financed. This is the total cost of the car minus any down payment. In this case, there is no down payment, so the amount financed is also \$18840.

Step 3 ：Finally, calculate the total installment price. This is the monthly payment times the number of payments. So, the total installment price is \$499.68 times 72, which equals \$35977.76.

Step 4 ：Thus, the total installment price is \(\boxed{\$35977.76}\).