I made an account, long time lurker, just to reply to this because I disagree with you on your last point regarding filing and doing menial work. To preface, I work for a major bank and have gone through a few internships in finance.

I'm not sure how internships work in your office but in banking internships only happen for 10 weeks during the summer months and that means that for around 42 weeks of the year you are working without interns. This means that for most of the year your full-time employees will be doing "menial" work because they won't have anyone to pawn it off to. The way I am understanding your company's culture it seems like you use these interns as a way to pawn off this work that you or your peers otherwise would normally do 42 weeks out of the year. This system works to help relieve some stress from your current full-time employees, but you have to understand that an internship is a recruiting tool. You may be thinking that an intern should be grateful for an opportunity to work for you, but the reality of it is that students/workers/interns can go find a different opportunity somewhere else. Why bother spending 10 weeks to train them and get them used to your culture if they don't want to come back? I sure wouldn't have gone back if filing was my main job.

Also, you mentioned that you were annoyed by your intern because it felt like "she was telling me I suck at managing people". Have you ever considered that you may not be the best at managing people? It sounds like you may be new to a management position and, as with almost everything, management skills have to be developed over time. If you think of interns as lowly filing monkeys that do things you don't want or have "time" to do, why does their opinion bother you?

Overall you gave some good advice but I hope that you understand that it's in your and your company's best interested to treat interns a little better, even if it is just for recruiting purposes. If anything do what the banks do, treat them nicely and take them to lunches during their internships and work them like a dog once they come back as full-time employees and slap them with a contract so they have to pay back signing bonuses if they leave.