Depending on the size of the fort, the basic cost of declaring a battle is as follows:
The funds will be taken from the treasury of the attacking city.
To prevent fake fort battles - where one alliance or player triggers multiple battles simultaneously to confuse the opponent - each subsequent attack triggered within 3 hours doubles the cost (this applies to all towns on the server). Outside the 3-hour interval, basic prices remain the same.
For example:
The formula for the increased price is:
price * 2n
where n is the number of battles scheduled within the previous 3 hours before the one you want to trigger.