Undergraduate research, writing a brief narrative?

Undergraduate research, writing a brief narrative?
An REU program I am interested in requires me to write a brief narrative discussing my goals and research interests. How long should this be and how should I start it? I have never written an REU paper before so I really don’t know what the recruiter looks for.

They want to know if you’re planning on going into graduate school (that’s a good reason for an REU at a college or university; if you want to go into industry, it might be a better option to look for an internship at a company) and if you’ve put any thought into the field you want to eventually work in. Talk about why you want to do an REU, what you hope to get out of it (experience, poster presentation, publication, etc) and why you’re applying to this one specifically (what interests you about the programs they offer).

If they list actual projects you can try to tailor your application to those, but for the most part they do NOT expect you to come up with a project on your own. This isn’t a research proposal, it’s an application essay.