Money can be a monetary or a non-monetary item

Fiat money can be either a nominal monetary item or a variable real value non-monetary item depending on where it is being used: inside the economy where it was created or outside.

Fiat money is a monetary item only within the economy where it is created. In this case, fiat money´s real value is eroded by inflation (low, high and hyperinflation) and increased by deflation within the local economy. 

The net monetary loss or gain in the real value of monetary items is not calculated and accounted under the historical cost paradigm during low and high inflation and deflation. It is calculated and accounted under the constant purchasing power paradigm required under IFRS in IAS 29 Financial Reporting in Hyperinflationary Economies during hyperinflation. 

Fiat money as a monetary item is generally never perfectly stable in real value over time during inflation and deflation. However, fiat money as a monetary item within the economy where it is created is assumed to be perfectly stable in real value by accountants, economists, business people and people in general for the measurement of many (not all) economic items under the historical cost paradigm, i.e., implementing the Historical Cost Accounting model during low and high inflation and deflation. 

When a country´s currency is used outside the economy where it was created, i.e., when it is used as a foreign currency in another economy, then it is a variable real value non-monetary item. The real value of fiat money used as foreign currency is determined in terms of other currencies in the multitude of foreign exchange markets around the world. A foreign currency´s real value in terms of other currencies is not determined just by the inflation rate in the economy where it was created, although this is an important factor taken into account by buyers and sellers in the forex market. Many other factors besides inflation or deflation are taken into account by buyers and sellers of currencies in foreign exchange markets when they determine the exchange rate of a foreign currency in terms of their own currency.

An entity with its head-office in a particular economy values the local fiat currency as monetary items under the historical cost paradigm during low and high inflation and deflation. Local currencies are always assumed to be perfectly stable in real value over time under the historical cost paradigm.  

An entity generally values foreign fiat currencies it holds as variable real value non-monetary items in terms of the constantly changing forex rates in the forex market. 

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