Using a similar application essay I used before I recently submitted an application essay for a pre-college program, and was accepted. I'm particularly proud of my essay; I put my best into it.

Now, after the pre-college program, I intend to apply for one of the institute's degree programs.

I've written an essay for the application. Most of it is rewritten, but it does have a lot of similarities (the intro paragraph is nearly identical). 


  Would it be considered plagiarism for using my own work? If not, is it still frowned upon if there are many similarities, and could impact my chances of getting accepted?


I understand that it is likely that answers are individual to each institute, but I'd like to know what the general answer is.

I've read some sources that claim students applying to multiple schools use very similar essays for all (assuming the prompts are similar), only changing statements specific to each school. So, maybe it is alright that I do such a thing? But then again, this is the same institute I'm applying to.
I honestly think there is nothing wrong in applying with a similar work of yours. And I think it, well, for all the reasons you've mentioned yourself, starting with the fact that it won't be considered as plagiarism, since the primary version of it is yours as well, ending with the fact that the work is sent to the same school.
However, depending on whether you've made only minor changes to it or not, you might adjust the work a bit more, or expand it, or formulate some thoughts differently for the sake of back-up (say, if there is a chance that any of the members of the admissions know or have previously seen your primary work - then they might think that you weren't generous on the effort and,therefore, don't perceive the opportunity to be worth working more on that work or on additional ideas). After all, you're the creator, so it is still up to you to decide upon all the abovementioned things!