The modern dollar sign is derived from what?

/* Spanish pieces of eight. */

There are a number of theories about the symbol's origin. The most common one, as cited in the Oxford Dictionary, is that the dollar sign is derived from the handwritten peso symbol that was used during the Spanish colonial era in the Americas. The symbol originally consisted of a paired script "PS", but gradually the "P" was written over the "S" with the loop of the P eventually disappearing as a matter of simplification.

The reason it was applied to US dollars is that Spanish coins circulated widely in the British colonies as well as those controlled by Spain. The most common coin was the famous "piece of eight", and it became the basis in both size and weight for the American silver dollar, thus its symbol carried over as well.

Other hypotheses

Some people have theorized that the sign was inspired by the double-pillar design borne by pieces of eight, but there's no definite evidence to that end. A few writers have also claimed that it's an amalgamation of "US"; however the symbol has been documented in books printed before the name "United States" appeared in the Colonies.

Origin of the Word "dollar"

Pieces of eight were one of several similar-sized silver coins that were issued by various European countries starting in the 15th century. They served as a (generally) common medium of exchange as market economies began to develop. However the name "dollar" didn't come from Spanish coins but rather from mines in central Europe.

Among these similar coins one of the most popular types was minted from silver found in St. Joachim's Valley in Bohemia. Today the region's part of the Czech Republic but at that time it was in the German-speaking part of the Holy Roman Empire. The Germanic Word for valley is Thal (or Tal in some spellings) which led to the the coins being called Joachimsthaler; roughly meaning "coming from Joachim's valley".

That mouthful was eventually shortened to simply Thaler, which is pronounced like the first two syllables of the English Word "tolerate". As Thalers spread to other countries the name was modified to fit local languages, resulting in tolar, daalder, and daler among others. Dutch merchants brought the latter spelling to North America where it was anglicized to the familiar dollar.