How will changing my major prolong my graduation time?

This is a good question for your university's academic advisers.

It really depends on your specific Uni/school, how far in you are, and what specific courses you've taken. If you're 1 year in, and most of the courses you've already taken are sort of general education requirements, then it might not add much time. If you're 3 years in and have taken almost exclusively poli sci courses that aren't required at all for fin, then it might add quite a bit of time.

It is difficult to give you a specific answer without more detail.

It is entirely possible that it is easy to figure this out from your college's website. For an example, look at UMich:

https://lsa.umich.edu/lsa/academics/degrees-requirements/academic-policies/credits-and-grade-point-average.html

You need 120 credits total.

Poli sci requires what appears to be 38 credits of poli sci (30 of which have to be 3rd or 4th year courses):

https://lsa.umich.edu/lsa/academics/majors-minors/political-science-major.html

So for example if you were in UMich and 1st or 2nd year, at most it'll set you 8 credits back, IF the finance degree doesn't require too many 1st & 2nd year courses.

Finally, another consideration is that if you're at a bigger university, you may need to apply to switch colleges (which may not be difficult, just extra process).

Best answer is to go ASAP to speak with counselor at the business school. But generally speaking you will have to take some business classes you didn't take as a Freshman, like pre-calculas, so you are behind. But, you can take classes over the summer to catch up. I think up to 4 classes per summer, or 12 hours.