Stephen Hutchison embarked on the drunken rant at a city centre flat, causing the pensioner to fear for her own safety.
Welfare workers were forced to call the police to the flat in Richmond Street when Hutchison’s behaviour did not cease, Edinburgh Sheriff Court heard yesterday.
He racially abused one police officer who arrived on the scene, also threatening to kill him.
Depute fiscal Iain Batho said the 38-year-old told welfare staff on November 4: “I am fed up with that old lady downstairs. I am going to kill her.”
Mr Batho said the woman was extremely distressed about Hutchison’s behaviour, adding that she “is in genuine fear for her life”, and had even contacted the procurator fiscal’s office on a “number of occasions”.
She has also installed an emergency alarm.
Hutchison, who is now living with his father in Penicuik, was fined £200. His solicitor said alcohol was at the root of his problems.
Sheriff James Scott told him: “You have come very close to being sent to prison.”