Am I kind of screwed if I want to go anywhere beyond Minnesota?

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Minnesota is 100% a no brainer.
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You still need to run the NPC…and indicate that you’re OOS, but ND resident. Even if you get a discounted rate or instate rate, you won’t be considered instate for AID purposes, so you may not get much/any aid…so much will depend on how much your family will pay each year.