Here is the new rule for raising armies, similiar thing is in for fleets:
1. The equation for army prices is: YOUR FACTIONS ARMY COST times HOW MANY ARMIES YOU ALREADY HAVE
Example: Egypt:
First army:
400 x 0 = 0
Second army:
400 x 1 = 400
Third army:
400 x 2 = 800
Fourth army:
400 x 3 = 1200

So if Egypt has 4 armies, they pay 0+400+800+1200=2200