I had a (short) paragraph with those things, saying why I wanted to go/why I'd be a good fit, but mine was mainly an update letter that I sent in late spring. The body of it was a paragraph updating them on my academic progress (i.e. "I am currently on track to receive A's in these classes"), and then a paragraph updating them on my research. For a letter of intent, rather than an update letter, the things you've mentioned are fine. If you can, though, I'd say something about what else you're doing (even if it's just a continuation of research/work/volunteering/whatever).