Faced with this stark choice, Osagie says she knew no one would believe her word against the lecturer's, so she recorded one of their conversations using a cell phone app.
The audio recording was leaked online and went viral on social media. Osagie says she did not leak it but had submitted it to university authorities before it surfaced online.
The student's allegations, coming amid the conversations around the global #Metoo movement, have now sparked a nationwide conversation in Nigeria about predatory sexual behavior on campuses and bolstered the notion that sexual harassment is a problem women the world over face almost every day.
In the recording, a man can be heard saying that if the student agreed to have s*x with him five times, he would improve her grades.
"Is it not five we agreed? Our agreement is five," the man says on the tape.
Osagie replies, "Is it B that you want to give me or A? Why would it be five times you will knack me? Prof, you know what? Let me fail it. I can't do it five times."
Student speaks out
In her only interview since the audio was leaked online, Osagie, 23, told CNN she had developed a mentor-mentee relationship with the professor after she helped him edit his book.
But the relationship soon made her uncomfortable because he started to make sexual advances towards her, she said.
"We actually edited the book together... Then, the next thing he told me was, 'Can you date me?' I was like, 'No.' He was like, 'Why?' I said, 'One, I don't date lecturers, and secondly, you are more matured than I am.'"
CNN hasn't been able to confirm the professor's age.
"He kept calling me to ask if I was ready to accept his proposal. So, I decided to record our next conversation," she added.
CNN has listened to the recording but cannot independently verify it. But a spokesman for the Obafemi Awolowo University (OAU) in Osun State, south west Nigeria, has confirmed that the voice is that of Richard Akindele, an accounting professor at the university.
The university said in a statement posted on its website: "Professor Richard I. Akindele, of the department of management and accounting, is now established to be the lecturer in the controversial "marks for sex" audio recording.
The female voice has also been identified as that of Miss Monica Osetobe Osagie, a postgraduate student on the Master of Business Administration Regular programme."
The OAU authorities say they have launched an investigation into Osagie's allegations and Akindele has been suspended pending a final decision by the university.
The university added that "it will continue to do everything legally and morally acceptable in pursuance of its avowed commitment to zero tolerance for sexual harassment, intimidation and, or coercion."
Akindele is yet to speak publicly and declined to comment to CNN.
"I have nothing to say until the university has concluded their investigation," he said.
Backlash on social media
Osagie says she has faced severe backlash since the university made her identity public when it released a statement.
"A guy came up to me at the bank and said, 'Is this not the girl who harassed a lecturer?' and he called me a prostitute. The security guard then had to push me away to go withdraw my money inside the bank," she said.
Osagie has also received abuse on social media and allegations that she tried to seduce the professor, she said.
Despite the criticism, Osagie says she has no regrets speaking about her experience. She hopes her case will give young women facing harassment on campuses the confidence to reject inappropriate advances from their lecturers, she said.
"I am actually happy I came out. I am helping many ladies that have gone through the same thing I have gone through, and most of them can't talk about it.
"They are scared of coming out in public. But I know it happens everywhere, not just in Nigeria. For me, speaking up will bring more women to speak and eradicate what is happening around young women and older men," Osagie told CNN.
"There is no work or ... education that is worth your dignity," she added. "I will keep saying that."
After the story broke in the media, Osagie faced a university panel investigating the allegations on the tape and is awaiting its findings so she can receive her certificate. There has been no suggestion that the findings will prevent her from receiving her degree.
Her lawyer, Abiola Akiyode-Afolabi, told CNN more victims have contacted her with allegations about the same professor since hearing about Osagie's case.
"We have ... a situation whereby people have promised to send to us affidavits ... where they can also give evidence against the professor," the lawyer said.
CNN has not been able to reach Akindele for comment about other accusers.
A spokesman for the university also told CNN the institution could not disclose whether other students had brought similar allegations against the professor.
"What is being investigated is the allegation leveled by the student against her lecturer. The university's council will make the final decision on the report the vice chancellor has submitted on the case," said Abiodun Olarewaju, a spokesman for OAU.
"This is because of the caliber of the lecturer involved," he added.
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