Strong book recommendation if you're interested in the topic.

http://www.amazon.com/The-Reckoning-Financial-Accountability-Nations/dp/0465031528

A surprisingly interesting read.

Fandorin is right to the best of my knowledge; Mesopotamians used something very much like a balance sheet in administering their empire.

I don't have an exact date range, but I did find this:

http://allmesopotamia.tumblr.com/post/32734961910/annual-balance-sheet-from-ur-louvre-museum

It's a stone balance sheet from Mesopotamia dating to ca 2000BCE.