MFE or other Options?

Hi all,

I'm a graduating senior in undergrad at a target school majoring in Finance and getting minors in Math and Computer Science. I'm planning on going to graduate school for a terminal Master's degree next year primarily for personal reasons. I've been able to secure an internship in trading (my intended career path) for the summer to bridge the gap until I complete another 1-1.5 years of school. I'd prefer to enter a competitive MFE program, but am worried about my chances given my non-STEM major. Should I feel comfortable that I'll get in to a top 20 or so program? If not, should I look for other options such as a regular Masters of Finance? Here's a bit on my background -

GPA - 3.9+
Math - Up through Calc 3, ordinary dif. eqs., linear algebra, probability and basic statistics
CS - 6 intensive courses, vast majority of experience in Java with a bit of experience in Python
One summer interning at boutique IB, other interning at non-finance non-profit

Long story short, I'm worried about lacking specific math (real analysis, pdes) or programming (C++) coursework from limiting my chances in admissions. Thanks in advance for any and all advice