<p>I honestly doubt a letter of interest would make that much of a difference. They know you are extremely interested in Yale if you bothered to apply early in the first place, and they state on their website that they don’t factor demonstrated interest into admissions decisions. Yale isn’t some community college where people apply just for a lark. The least of their worries is finding students who are deeply committed to their institution. You’d be better off having your guidance counselor call and ask where your application was weak, and firming up those areas if you can.</p>