Noarchive meta tag will not affect the page rank or It will not penalize your page.
An article from SEJ saying,
Can you get penalized for using noarchive on your pages? – Apparently,
no. But some people treat sites with unavailable cache version with
suspicion: “when I see pages not cached my first thought is that
they’re cloaking“. SEO rumors never stop, and one of them has it, that
noarchive used to be a red flag – I personally don’t think so.
Officially, Google also states, there’s nothing wrong with webmasters
using the tag:
This tag only removes the “Cached” link for the page. Google will continue to index the page and display a snippet.
So if you use
Noarchive meta tag in a page you don't need to worry about the SERP of that page.