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I think it depends. If you browse open positions, you'll see that many finance and accounting positions ask for a finance or accounting degree. If you want to be an accountant, you definitely need those core accounting classes for fundamentals. Finance classes usually help to develop a slightly different skill-set, such as financial modeling and analysis.
It is a huge advantage to be proficient and both accounting and finance, but you may not need to get an additional degree in finance in order to accomplish this. You'll want to see how much longer it would take you to get that additional degree and the cost of it. An extra couple of classes may be worth it, but an entire semester or year can be costly and time consuming. You might look into a minor, a concentration, or just taking finance classes as electives. Most business degrees require you to take a couple elective courses, so you could focus on finance classes for those.
Whatever route you pick, I would definitely stress the importance of having advance Excel skills. Strong Excel skills will definitely open up opportunities and this is something you can pick up informally, for little or no cost. You can develop Excel skills independently but I would also see if your school offers a course as well.
Yes, extra courses, minors, double majors, an extra emphasis, etc are almost always beneficial. Having a strong academic background in both accounting and finance just expands the entry level as well as advanced opportunities in these fields. Also you are often required to have specific courses for professional exams in finance or accounting fields and having them in college would speed the process.