Financial evolution means that monetary arrangements obtain a higher level of complexity, including more sophisticated monetary heuristics. This chapter provides a plausible cognitive-behavioral explanation of cashless payments systems—accounting systems of exchange—in terms of perceived purchasing power of currencies as reflected in exchange rates. It considers the historically specific context of Amsterdamsche Wisselbank and Stockholms Banco, by describing the economic context of these two banks, before studying the evolution of exchange banks in the sixteenth century. Stockholms Banco was the first European and Western bank to issue banknotes, the first outside China, but excessive note issuing forced it to close and be turned into the Swedish central bank, under the Swedish Parliament. The monetary environments in Amsterdam and Stockholm differed. We may contrast Dutch order, where Amsterdamsche Wisselbank had a coordinating function, with Swedish mess, which was both the origin and end of Stockholms Banco.