If SAI is 17k, then the federal govt estimated that you can afford to pay 17k based on your income. That's not the same as what colleges may think you can pay after considering your assets.
Use specific college Net Price Calculators (NPCs).
By the way, 17k won't cover room and board. The way you asked this question makes me wonder if you have a typo, and meant to type 170k, which would be very likely full pay, but again, use those NPCs. You can enter the info anonymously.