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Is it ok to keep interviewing if I accept a post-graduation offer?

Here's my situation, let me know what you guys think.

Educational Background (for reference):
Undergraduate Mathematics Student, GPA, 3.9+, Mid-tier university . Current Senior, graduating Spring 2018.

I recently completed a Quantitative Analyst Internship with a major US bank, and received an offer to work full time for them post graduation. They have given me up until the second week of September to make up my mind. My total pay for the first year would be $70,000. The company is in a lower cost market than NYC.
I am a little concerned that the offer is way too low, and after contacting the company, they aren't willing to raise the offer. According to PayScale.com, on a national scale, the median entry level base pay for a Quantitative Analyst is about $78,000.
Notice that's base, and my offer is total pay. I want to keep applying to other firms to see if I can land a more competitive offer, but I am concerned that if I reject theirs, since Quant Jobs are hyper competitive, I may not get anything else. I am considering to just accept their offer, but keep applying to other firms regardless. If I do so, what is the possibility that the firm I am applying to will found out, or the firm whose offer I accepted will find out? Is it worth it?
I understand some people may say since I am an undergraduate and managed to secure a Quant Job, that I have nothing to worry about if I cast my net (considering how hard it is to get a Quant Job without a grad degree). Last summer I tried applying for over 50+ Quant internships, and could only get a single offer. If I were to begin applying again, would it do me any good to apply twice to the same firms that rejected me previously? Since someone else was willing to give me a chance, perhaps in their minds they will think they overlooked something, or I acquired new and useful skills? But they will also probably want to ask if I received an offer. What do I say if they ask this?
Additionally I am in the sticky situation of having north of $100,000+ of student loan debt, and my family makes under $30,000 per year. Financially speaking, I can not afford to get this wrong.

What's the best move? Accept but keep applying, Accept and go work for them for a few years, or Reject and see if I can get a better offer.

I am sorry for being so verbose. There are a lot of angle's to my current problem. Also I apologize for being slightly vague in my details, I do not wish to identify myself.