Good evening, Phanghor.
I've just had to re-type part of this as I discovered that I was typing in English with my keyboard set to Greek. Hence I was writing fluent gobbledegook... Nothing new there, I hear people say!
Anyhow, I suspect it depends on context. I would normally expect it to refer to an internal process within an organization, or something that has an aspect of scrutiny, however. I might "render" my Travel and Subsistence account to my employer's finance department, and yes, that would be to have it paid (hopefully). Then again, I suppose a company might "render" accounts to a regulatory authority to which it is subject. And there is no particular reason that I can think of why the word could not be used to refer to sending an account to an outside organization or person from whom payment is expected. It just seems a little "over the top" in that context.
It's really a rather formal synonym for "to submit" (i.e. for payment or inspection).
Simon.
Έτσι είναι η ζωή!