Hello,
I will be completely frank and honest with you, even if it might offend you, because what I am about to say is in your own interest:
If you are not aware of this, you should be that the publicly visible Google PR does not change or update at any fixed or regular intervals. Google used to do this approximately one a month earlier, but for many years now, they have stopped doing that. Currently, it is not predictable when they will make the next update of the PR, so expecting a PR increase in a 'short time' is unrealistic.
Having said that, if the end result of PR you expect is ranking boost for your site, this can happen in a short time period, ranging from 2 or 3 weeks to 6 or 8 weeks.
I will be happy to acquire high quality links for your website to boost rankings and eventually, this will also result into a PR increase at a future date.
Kindly review my profile and if you find me suitable for the job, please message me here to discuss this further.
With best regards,
Richa Varma
BE(IT), MBA(Marketing)
Freelancing Web Tech/Dev WAHM
ps. In light of the Additional Project Description you provided recently, my suggestion is to delete the project - rankings are all that matter, more than 95% of all Internet users have never even heard of PR and chasing PR is a 'pipe dream' :-)