According to Wikipedia, there were a wide range of currencies in the Middle Ages:

The various Germanic states in the west all had coinages that imitated existing Roman and Byzantine forms. Gold continued to be minted until the end of the 7th century, when it was replaced by silver coins. The basic Frankish silver coin was the denarius or denier, while the Anglo-Saxon version was called a penny. From these areas, the denier or penny spread throughout Europe during the centuries from 700 to 1000. Copper or bronze coins were not struck, nor were gold except in Southern Europe. No silver coins denominated in multiple units were minted.

Say that someone had one of these forms of coinage (such a local German state's coinage, or some coins minted by a local ruler). That person then travels to a far off region and wants to spend their coins at a local inn, but the people have never seen those coins before. How would currency exchange be negotiated? Or would the coins in the new region be considered worthless?

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In principle, a coin is worth its value in precious metal, plus or minus what the locals think of the issuing authority. So an unknown silver coin weighing half an ounce would be worth 'half an ounce of silver in local coinage' less the expected costs of melting it down and re-coining. The Vikings, who didn't use coins as such, used 'hacksilver' as an intermediate stage between barter and coinage: if you agreed to pay an ounce of silver but only had a four-ounce candlestick, you cut a quarter off it with a hacksaw.

This is obviously unsatisfactory for any form of long-distance trade, so there were professionals called money changers, who would inspect a foreign coin and buy it for its value in local currency, less a percentage to cover the moneychanger's expenses. ("Money changers would assess a foreign coin for its type, wear and tear, and validity, [and purity, presumably] then accept it as deposit, recording its value in local currency", Wikipedia). Obviously, if the moneychanger could then sell the coins to somebody travelling in the right direction, a double profit could be made. Often, the moneychangers were Jews, who were often barred from owning land, had a high literacy rate and maintained contacts with co-religionists in other areas; the network could be regarded as a rudimentary banking system.

OF course, in the fifteenth century there arose proper banks, who would issue letters of credit when you paid into your local office, redeemable at your destination in local currency. (The Knights Templar did something similar for pilgrims around the time of the Crusades; but after they were suppressed for idolatry (oddly enough, by one of their debtors) the idea fell out of favour for a few centuries).

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