It's a bit tough to give you thoughts on your overall candidacy without knowing more about you (work experience, demographics, etc) but here are some thoughts on that low GPA! You made a HUGE improvement, which is awesome. I'd definitely use the optional essay to highlight that & to point to the fact that your later years (and hopefully your work experience) are more representative of your abilities. I wouldn't necessarily talk about the switch from engineering to finance as the REASON for your improvement though. Even if engineering wasn't your thing, the adcom is still not going to agree that a 1.47 GPA is acceptable & you don't want to make it sound like being uninterested in a topic is a good excuse for performing so poorly. When you explain a low GPA it's critical to take ownership of it & make sure you don't sound like you're blaming it on anyone or anything. You COULD say you made bad choices (about how to prioritize your time, etc) and that in addition to switching to a major that was a better fit for you you also learned to make more responsible decisions and gained maturity. Then you're taking ownership while at the same time pointing to the ways in which you learned from your mistakes and changed.
Like I said, it's hard to say what your overall chances without knowing more about you, but you will want to err on the side of applying to schools where you exceed the GMAT average. They will be looking to the GMAT (as well as your work experience like I said) to compensate for that low GPA. Even though you ended on a high note with the GPA (which again is great) those early years will be a bit of a weakness in your overall candidacy.
Hope that helps!