Final answer:
The modern Canadian banking system started with the Bank of Montreal in 1817, which is the oldest bank in Canada.
Step-by-step explanation:
The modern Canadian banking system began with the founding of the Bank of Montreal in 1817. This institution was established before other banks listed in the options, such as the Chartered Bank of Upper Canada in 1821 and the Bank of New Brunswick in 1820.
The Bank of Lower Canada, another option provided, was also not the beginning of the modern Canadian banking system. The Bank of Montreal is significant for being the oldest bank in Canada and it played a crucial role in the development of the country's financial structure.