How much money do you need to open every fairy fountain?

The first Fairy Fountain will cost 100 rupees, the second 500, the third 1,000, and the fourth will cost you 10,000 rupees.

In addition to @Yuuki's answer, there is a fifth Fairy Fountain which costs 1 000 rupees to open.

That fountain looks just like the other 4 fountains, but is quite special indeed.

It is found at Malanya's Spring near the Lake of the Horse God which is just behind the Highland Stable. Its purpose is to revive any horse you have registered that has died during your adventure.