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We should note that there were three different currencies in circulation in NT times, and each are mentioned in the gospels: Jewish, Greek and Roman.
The way the name of the coin is translated into English varies in different translations of the Bible. Because of rapid currency fluctuations and inflation, it is not always helpful or meaningful to translate the coins into their direct English equivalent. However many versions of the Bible provide a footnote with the Greek name of the coin.
The list below shows the different coins in circulation in ascending order of value, and notes some of the places where they are mentioned in the NT. The Greek word for the coin is in brackets.
Lepton (lepta) - Greek
The Lepton was the lowest value Greek copper coin, with equivalent value of half a Roman Quadrans
The widow’s two small copper coins (lepta) (Mk 12:42, Lk 21:2). Mark actually gives the conversion rate between Roman and Greek currency.
Pay debts to the last penny (lepton) (Lk 12:59)
Quadrans - Roman
The Quadrans was a Roman copper coin, with equivalent value of two Greek Lepta
Widow’s two small copper coins (lepta), worth a penny (quadrans) (Mk 12:42)
Pay debt to the last penny (quadrans) (Mk 5:26)
As or Assarion - Roman
The Assarion was a Roman copper coin, worth eight Roman Quadrans
Are not two sparrows sold for a penny? (assarion) (Mt 10:29)
Are not five sparrows sold for two pennies? (assarion) (Lk 12:6)
Drachma (drachmae) - Greek
The Drachma was a Greek silver coin, with equivalent value to a Roman Denarius
The woman’s lost silver coin (drachma) (Lk 15:8)
Denarius (denarii) Roman
The Denarius was a Roman silver coin, worth 16 Roman Assarions, and equivalent to a Greek Drachma. It was the daily wage for a labourer.
The daily wage for a labourer (denarius) (Mt 20:9-13).
The two coins the good Samaritan paid the innkeeper (two denarii) (Lk 10:35)
The unforgiving servant was owed 100 denarii (Mt 18:28)
The tax paid to the emperor (denarius) (Lk 20:23)
Didrachmon - Greek
The Didrachmon was a Greek silver coin, with equivalent value of two Roman denarii
The temple tax (didrachma) (Mt 17:24)
Shekel - Jewish
The Shekel was a Jewish silver coin, with equivalent value to one Greek Stater, or Tetradrachmon
Stater, or Tetradrachmon - Greek
The Stater was a Greek silver coin, worth four Greek Drachmae or four Roman Denarii
The temple tax found in the fish’s mouth for two people (stater) (Mt 17:27)
Judas’ thirty pieces of silver? (Mt 26:15)
Aureus (aurei) - Roman
The Aureus was a Roman gold coin, worth 25 Denarii
Take no gold? (Mt 10:9)
Mna, or Mina
There was no coin for a Mina, which was worth 100 Greek Drachmae, or four Roman Aurei
Parable of pounds (minas) (Lk 19:13)
Talent
There was no coin for the talent, which was worth 60 Minas or 6000 Denarii
Parable of talents (Mt 25:14)
The unforgiving servant's debt of 10,000 talents (Mt 18:25)
Modern values
The modern value of the coins can be approximately calculated from the fact that a denarius was a day's wages for a labourer. This is indicated by the parable of the workers in the vineyard, who were all paid a denarius (Mt 20:1-16). The modern equivalent of the worth of a denarius in the U.K. (a day's wages for a labourer) in the early twenty-first century could be considered as being about £72 (8 hours at £9 per hour), giving a salary of about £15,000 per year. So, the debt of 10,000 talents in the parable of the unmerciful servant (Mt 18:21) was equivalent to around 300,000 years salary, a modern equivalent of £4 billion - an unimaginable personal debt, and great forgiveness.
There are many web-sites with photographs and descriptions of coins in circulation in the first century.