Should I undercharge for freelance work in the hopes of getting more work?

I’m a college student, and I have a very part time internship gig with a documentary filmmaker—writing up grant proposals, updating her webpage, etc. For the past few weeks, I have been working on a page and a half long proposal to get funding for something, which has involved my having to interview someone twice via phone, do research on statistics, and write a couple of drafts.

I added it up, and I spent 7.5 hours on this project. I’m being paid $10/hour for my work. She asked me to send her an invoice. Should I charge her for the amount of time I actually spent on this? Or should I say I spent less time? I’m worried she’ll think it’s too expensive to hire me or I work too slowly.