Time is valid

Hi all,

First of all I've used JR pass on the past but the deal is that I remember that, when I did I had some issues with the period that it was considering valid (As I remember I think that I did a mistake and it lasted shorter than I calculated...)

Anyway, since I'm going to use it again and I want to avoid that mistake I want to ask. I'm arriving at Narita in 24/9 and I'm departing in 8/10 okay? So if I'll purchase a 14 days JR Pass and validate it on 24/9 it will last until 7/10 twelve in the midnight? Or until 6/10 twelve in the midnight?
I know it might be silly questions but I need to clear my concerns and be sure this time.

Thank you for reading, I would appreciate your help! :)