Incan Currency: They didn't have one! They didn't understand money, but they traded things. gold was their favorite metal because of its colour. They worshipped the sun and they thought it was a god. They did have one thing they used as money. Woman would trade cloths (like money) for other luxury items such as gold and jewels or clothing. Trading with cloth mostly happened among woman of the Inca.
Inca were masters of city building but nevertheless had no money. In fact, they had no marketplaces at all. The secret of the Inca's great wealth may have been their unusual tax system. Instead of paying taxes in money, every Incan was required to provide labor to the state. In exchange for this labor, they were given the necessities of life. Of course, not everybody had to pay labor tax. Nobles and their courts were exempt, as were other prominent members of Incan society.
In another quirk of the Incan economy, nobles who died could still own property and their families or estate managers could continue to amass wealth for the dead nobles. Indeed, the temple at Pachacamac was basically a well-managed estate that "belonged" to a dead Incan noble. It's as if the Inca managed to invent the idea of corporations-as-people despite having almost no market economy whatsoever.
One of the outstanding questions for scientists and historians who study the Incas is why this wealthy, sophisticated culture developed scientifically and culturally without ever inventing markets. One possibility is that life was so difficult to sustain in their environment that all their innovations revolved around agriculture rather than economics. In other words, the Inca Empire was optimized to prevent starvation rather than to foster trade.
In the case of the Incas, it's likely that the technologies that granted them agricultural surplus (extra food and textile materials) helped them with their expansive empire-building. Food was their coin; pure labor structured their economy.