Verified Certificate

Supported by the following organizations

This is to certify that CARLOS ALBERTO ARAGON DE PLANAS successfully completed and received a passing grade in 15.431x: Fundamentals of Entrepreneurial Finance: What Every Entrepreneur Should Know a course of study offered by MITx, an online learning initiative of the Massachusetts Institute of Technology.

Noted by

Antoinette Schoar

Antoinette Schoar

Stewart C. Myers-Horn Family Professor of Finance and Entrepreneurship, MIT Sloan School of Management Massachusetts Institute of Technology

Bill Aulet

Bill Aulet

Managing Director of the Martin Trust Center for MIT Entrepreneurship and Professor of the Practice, MIT Sloan School of Management Massachusetts Institute of Technology

Matt Rhodes-Kropf

Matt Rhodes-Kropf

Visiting Associate Professor in the Finance Department, MIT Sloan School of Management Massachusetts Institute of Technology

Sanjay Sarma

Sanjay Sarma

Vice President for Open Learning Massachusetts Institute of Technology

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About edX Verified Certificates

An edX Verified Certificate signifies that the learner has agreed to abide by the edX honor code and completed all of the required tasks of this course under its guidelines, as well as having their photo ID checked to verify their identity.