At your age, kids tend to heavily discount the future. I know I did. But to get a name school on your resume/OCR at a target school, saving your money for a Masters like that Duke program (there are others like it and more quantitative ones) or top MBA may be more cost-effective.
I won’t say it’s a slam dunk because BC would offer a BC undergrad experience (grad school isn’t exactly the same, though could be similar).
I would say that both BC undergrad or a Masters at a target school could get you where you want to go and it seems that you have enough money to only spend on one of them. 20/40 years from now, the expense/ROI won’t be what you will think about. Instead, it will be the experience. So have you visited BC? Do you have a burning desire to be an Eagle (I can’t say I sense that; especially since you are asking strangers on the internet). If you don’t, does spending extra on BC make sense? Especially since it is possible to break in to IB from a non-target, even if it is tougher, but if you manage that, the $100K or so you saved could turn in to a decent sum after 20/40 years of compounding investment returns.