Alexander hamilton believed that a national bank would

Hamilton believed a national bank was necessary to stabilize and improve the nation's credit, and to improve the handling of the financial business of the United States government under the newly enacted Constitution.

d. i assume the underlined word is "role." reformat if it isn't.

explanation:

role is closest to part because when replacing words, "playing a vital decision," "playing a vital activity," and "playing a vital dollar" don't make logical sense. the only meaningful choice is "playing a vital part."

this fits one of merriam-webster's definitions of role: "a function or part performed especially in a particular operation or process."