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Among the many differences, Alexander Hamilton and Thomas Jefferson had, one of the most notorious was the issue of the National bank of the United States.
During the presidency of George Washington, Alexander Hamilton, the Secretary of the Treasury, believed in the necessity of having a national bank. On the other hand, Antifederalist Thomas Jefferson considered that this would give the government too much power and could generate a monopoly that affected private banks in the country.
The situation increased in tension when Thomas Jefferson declared that the national bank was anticonstitutionalists because the United States Constitution never mentioned that the federal government had the power to create one.
The response of Hamilton was immediate. He stated that the bank indeed was constitutional because the US Constitution gave Congress the power to coin money, borrow it, collect taxes, and also regulate national and foreign trade.