In The Wheel of Time, the Aes Sedai seem to travel throughout the entire main continent (up to the Aiel Waste), and from what I have seen, have absolutely no concern for money. They also seem to be tasked with bringing back any women with the potential to channel the One Power to the White Tower in Tar Valon.
In the White Tower, the recruited women are trained to use the One Power, and the ones who complete the training go on to be Aes Sedai. This training process can easily take over a decade on its own, depending highly on the ability the woman has with the One Power.
We never hear Moiraine or anyone at the White Tower discuss tuition with the girls that I remember. Given the way Moiraine discusses how few novices they have, and the lack of payment mentioned, I assume that the White Tower pays for the teaching while one is an Novice and Accepted (if not paying for the women afterwords).
I'm thinking the White Tower must have a large amount of money. The only other remotely plausible explanation that comes to mind is Moiraine is rich due to her noble past, and paid for the girls to attend the tower behind the scenes. That seems unlikely to me though.
So to summarize: how did the White Tower/Aes Sedai have so much money?
(I'm not going to lie, this is a blatant rip-off that came into my head when I saw a very similar question about ASOIAF on the Hot Network Questions and realized this is something I've never seen the answer to)