Bala Chinda, 26, is alleged to have killed 36-year-old escort Nkechi McGraa - also known as Jessica - at a flat in Union Terrace in February 2016.
Advocate Depute Paul Kearney said there was overwhelming evidence against him.
However, defence counsel Ian Duguid said the prosecution had not proved guilt of rape and murder.
The trial, at the High Court in Aberdeen, continues on Thursday.
Closing speeches have been heard in the trial of a man accused of raping and murdering a woman in an Aberdeen city centre flat.