Final answer:
Democratic-Republicans initially opposed the National Bank but supported creating the Second Bank of the United States in 1816 due to the economic pressures of the War of 1812.
Step-by-step explanation:
The Democratic-Republicans initially opposed the creation of the National Bank of the United States, which was central to Alexander Hamilton's financial plan for economic stability. However, during the severe economic strains of the War of 1812, recognition of the need for a robust national financial system led to a reevaluation.
When the charter for the First Bank expired in 1811, it was the difficulties of funding the war that convinced then-president James Madison, along with Congress, to create the Second Bank of the United States in 1816.
The establishment of the Second Bank was met with opposition from states that felt it represented too much federal control, a view that intensified when Nicolas Biddle began curtailing the government's influence over the bank in 1823.
Despite this background, no direct exchange or compromise is widely recorded as having occurred for Democratic-Republican support in creating the National Bank. Instead, it seems economic necessity eventually overrode earlier ideological opposition to central banking.
As elements within the Democratic-Republican party evolved, and the Second Party System emerged, one faction became the Democratic Party, which under Andrew Jackson adamantly opposed the National Bank.
Nevertheless, despite Jackson's dismantling of the bank during his presidency, the initial creation of the Second Bank in 1816 under Madison was a response to the economic hardships and the limits a fragmented banking system placed on national growth and stability.