Dear [Hiring Manager's name],
I am a second-year computer science student at [University], applying for [Company]'s [Software Engineering Internship]. Last year I built a course-scheduling web app because planning a week at [University] meant checking four different pages. Roughly 300 students now use it, and I handled the authentication, database design and deployment on my own.
The rest of my evidence comes from building with other people under pressure. At a national hackathon my team placed third of 40, building a working prototype and presenting it to judges within 36 hours. In a group capstone, we delivered a donor-tracking tool for a local charity that is still using it a year later. I have also had three pull requests merged into an open-source library, including a fix for a race condition in its caching layer.
I am applying to [Company] specifically because [one concrete reason you can check — for example, your interns ship to production in their first month, as described on your engineering blog, or you build the [product] I already use for [purpose]]. After running my own app for real users, I want to spend a summer learning how an engineering team does the same thing at scale.
Alongside my degree I have worked 15 hours a week in retail throughout term time while keeping a first-class average, so I am used to managing a full workload reliably. I am available full time from [start date] to [end date], and could [start a week earlier / work remotely for part of the placement] if that helps your planning.
I would welcome the chance to talk about the internship. Thank you for considering my application.
Kind regards, [Your name]