Verified Certificate

Supported by the following organizations

This is to certify that Pranav Ravikumar Patil successfully completed and received a passing grade in 15.415.1x: Foundations of Modern Finance I a course of study offered by MITx, an online learning initiative of the Massachusetts Institute of Technology.

Noted by

Leonid Kogan

Leonid Kogan

Nippon Telegraph & Telephone Professor of Management, MIT Sloan School of Management Massachusetts Institute of Technology

Jiang Wang

Jiang Wang

Mizuho Financial Group Professor, MIT Sloan School of Management Massachusetts Institute of Technology

Egor Matveyev

Egor Matveyev

Senior Lecturer, MIT Sloan School of Management Massachusetts Institute of Technology

Krishna Rajagopal

Krishna Rajagopal

Dean for Digital 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.