A graduate of Brown University, Dexter was admitted to the bar and briefly practiced law before turning to business and financial speculation.

Around 1805 he conceived the idea of a large office building with public meeting space, and began construction of the Exchange Coffee House in Boston.

Dexter resorted to printing massive quantities of worthless bank notes to pay for construction and operation of the building; when his fraud was uncovered, he lost control of the venture and fled the country to escape his creditors.

[5] In his concept, the Exchange Coffee House would also provide a service by helping establish the relative value of the bank notes of the various financial institutions in and around Boston.

[5] Traders in bank notes in the Boston area set the local discount rate by conducting business in outdoor meetings on several city streets.

[7] In 1807 President Thomas Jefferson implemented an embargo against Great Britain and France as a protest against violations of American neutrality during the Napoleonic Wars.

[8] In addition, the traders in bank notes whom Dexter hoped to entice into the Exchange Coffee House to conduct their business preferred to continue working outdoors, so he did not realize the increased customer traffic and rents he anticipated.

[5] As a result, shopkeepers began to refuse the bills issued by Dexter's banks, meaning he could no longer pay suppliers and workmen.

[14] At the 1817 auctions in Milledgeville, Georgia, which followed the end of the War of 1812, Dexter bought several hundred acres on the east bank of the Alabama River near a Creek Indian trading post, where he founded a town called New Philadelphia.