I purchased a few PR3 - PR5 links yesterday but haven't seen any updates for my site on Google Pagerank's backlick checker nor iwebtools. How long is it supposed to take..?
You won't see them for a while at least till the SE's update their backlinks. Google is especially slow doing that and most likely will be months.
Alexa is even slower, according to them I've only had 2 backlinks in over 2 years... not great odds Though redgsr is correct. However, I'd like to add that it can take even longer depending on when you get the link and where...as indexing has to count for something. If it is on a slow moving site, Google may not find it for months, then once it's found it has to wait even more months for the actual update to happen.
For the links to take effect on your backlinks, it's usually around 3 months or until Google updates their pagerank, which from the current trend takes around a month.
I have noticed my backlinks improving my SERP's within 24 hours here recently. Now whether Google actually shows them or not is a different story. Most websites are crawled rather frequently though once indexed so your link building should have fairly quick results.