how do passwords work?

newbie here. so consider this paradox: let's say you have a pass protected rar file. now the password should be stored somewhere in the file to compare against the inputted password. so if it's there how come you cant just extract it?

I don't know anything about RAR encryption beyond the fact that it uses AES, but I'm assuming it just tries to decrypt with the password the user provides and errors out when the first few blocks don't form a legitimate RAR header. That would make a lot more sense than storing the password in the file, which would be a retarded idea..