Currency

When bartering for goods and services no longer meets the needs of commerce, the sentient beings of the Realms turn to using items with a more universal value, namely precious metals, gems, and some minerals. Metals are rarely found in their pure form in nature and require significant energy and effort to refine and purify them. In general, the rarity and the amount of effort it takes to produce a given metal determines its worth. Sometimes this formula is modified by a particular property of the metal, or by a widespread use (and therefore greater demand). The penalty for counterfeiting is death in most places because cities, kingdoms, and nations rely on the acceptance and trust of their currency.

Gems are even rarer than metals and require great skill in mining, cutting, and polishing. Gems have great value because people desire them for their beauty and often wear them in jewelry. The arcane Arts also require certain gems as spell components which increases their rarity even more as they are consumed in the casting of powerful spells.

1st Edition Currency
In the 1st Edition Forgotten Realms Campaign Set the kingdom of Cormyr is used as a representative example of a location with a standard system of currency. The names and values of the various coins are:

This valuation system is prevalent but not ubiquitous throughout the Realms.

Cormyr
The royal coinage of Cormyr is stamped with a dragon on the obverse and a treasury date mark on the reverse. There is no paper currency other than I.O.U.s which are known as "blood-notes" because they must be signed in blood by all parties involved and taken to the local Lord for the affixing of the royal seal.

2nd Edition Currency
The 2nd Edition Forgotten Realms Adventures source book states that the FR uses the standard rates of exchange between coins as noted in the Player's Handbook 2nd edition :

Copper
Copper coins are known as coppers, copper pieces, or, in Cormyr, copper "thumbs". Sembia released a square iron coin called the steelpense which is similar in value to the copper. In the south, Amn mints copper fanders and Calimshan produces copper unarches, radas, niftens, and spanners.

Silver
Silver coins are known as silvers and silver pieces. Cormyan silvers are known as falcons and Sembian silver coins are triangular and called hawks. The two coins are used interchangeably. Amn mints silver tarans and Calimshan makes decarches, espedrilles, and the ochre-tinted red worm of Memnon. Red worms are cast from silver and then coated with a dye. Old coins with the dye worn off are called "skinned worms".

Electrum
Electrum coins are not as popular and gold, silver, and copper, but do exist and are commonly called blue eyes throughout the heartlands of the Realms. Cormyan eyes are round, Sembian electrums are diamond-shaped. Amn produces electrum centaurs and Calimshan has tazos and zonths. The electrum moon of Silverymoon is an exception, being worth 1ep throughout the Realms but double that in the Silver Marches.

Gold
Gold coins are the most common coin used by adventurers and are often called golden lions although only the Cormyan coins are stamped with the figure of a lion. Sembian gold coin designs vary from year to year but are always a distinguishing five-sided shape. Amn mints the gold danter. Due to upheaval in Tethyr, Tethyan gulders, moelans, myrats, and zoths are only worth 60-90% of their usual value.

Platinum
Platinum coins are called tricrowns, plats, or pearls (in particular the Southern versions, which are officially named roldons). Sembia produces no platinum coins but readily accepts those of other nations.

Other Currency

 * A Waterdhavian toal is worth 2gp in Waterdeep and practically nothing elsewhere.
 * A Waterdhavian Harbor moon is a special coin in the shape of a cresent, made of platinum and inset with electrum. It is used in bulk purchases in Waterdeep where it is worth 50gp.  Outside Waterdeep the value drops to 2gp.
 * Bela is paper money used by barbarian tribes to the east in Kara-Tur. In western Realms it is worthless and occasionally offered as an insult.
 * Blood Notes are scrolls, letters, or other carvings representing I.O.U.s and promissory notes from the listed person(s) to the holder of the note. Blood notes can be offered by individuals, adventuring companies, or countries and cities to cover debts.  In common usage the debtor is legally obligated to pay when the note is presented.  Blood notes from deceased individuals are not binding.
 * Trade bars from (Mirabar) are made of black iron and shaped like rectangular spindels(sic). They are worth 10gp in Mirabar and 5gp in the rest of the Realms.
 * Trade bars from merchants are thin silver bars marked at one end with the value, typically 10, 20, or 50gp, and the other end has the symbol of the trading institution or coster which created it. An increasing number of these bars bear the mint mark of Baldur's Gate.  Trade bars of the Iron Throne trading group are not honored by other trading organizations because this group is considered disreputable.  Broken trade bars have no value but most merchants will continue to honor the trade bars of defunct institutions.
 * Trade bars from Sembia are ingot-shaped silver bars dotted with copper and the Sembian symbol. They are considered "face value" and typically come in 5, 10, 25, and 50gp denominations.
 * Trade bars from Lantan are flat envelope-shaped bars of worked steel marked with the great wheel of Gond. They are worth 20gp each and used primarily along the Sword Coast.
 * The Sembian steelpense was introduced by the Sembian government to replace the silver piece but was overproduced and the value has dropped to 1cp.
 * Shou Lung copper is any copper coin which is not immediately recognizable and therefore declared to come from the mystical East and is given a value of 1cp. Only a small number of these coins actually come from Shou Lung, or any of the Kara-Tur nations, but the name stuck.
 * Shou Lung silver is similar: any unknown or badly worn silver coin given a value of 1sp.
 * Trade bars from Shou Lung are slender bars of silver, definitely oriental in origin, that have made their way to the West. Shou Lung trade bars are worth about 40gp each.
 * a Letter of Trade is similar to a Blood Note and calls for a delivery of a particular item or items to the bearer.
 * Tharsult Statues are small art objects used in trade. They are made of ivory, jade, or serpentine and are used as coinage in that region.  Most of these that reach the North are treated as curios and are worth around 15gp.  In their native land they are worth about 5gp each.
 * Shaar Rings are made of sliced and bored ivory and hung on long strings by the plainsmen of Shaar. Rings will be found in bundles, and each ring will be worth 3gp each.
 * Gond bells were introduced by the Lantanese and used in regions of the North, in particular in trade between worshippers of Gond. The small brass bells enclose a lose ornamental stone which causes it to clatter.  Each is worth 10gp on the open market or 20gp if traded to a church of Gond.
 * Mercenary Cards are small cards of parchment about the size of a Talis card, marked on one side with the symbol of a particular mercenary company. The reverse is usually a handwritten scrawl from the troop's paymaster authorizing payment.  These become currency by being found in loot caches, won in card games, or stolen from the unwary.

Silver Marches (Luruar)
Silverymoon mints its own coin, the moon. It is valued at 2gp and is accepted throughout the Silver Marches.

Waterdeep
In Waterdeep a toal is a coin that is worth 2gp in the city but practically worthless outside the city. The toal is a square brass coin with a hole in the center to allow it to be strung on a string.

4th Edition Currency
The platinum coin of Waterdeep is known as the Sun.