How legitimate is the National Academy of Future Physicians?

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It's "legitimate" in that it's not a scam - if you pay the money, you'll get to participate in the program.

That said, it's not an honor, you weren't nominated, and it amounts to basically a very expensive vacation. It won't help your college applications and actually might hurt them - admissions officers know this is a vanity award at best, so broadcasting yourself as gullible and naive might actually make them less likely to accept you.