Sandeep Patel was quizzed by police after the body of 97-year-old Annie Temple was found at her home in Kinglassie, Fife on October 25 2019.
The 38 year-old is on trial at the High Court in Glasgow where he denies killing her.
Jurors heard on Monday how Patel gave a statement to a constable on the day of Annie's death at the home in Cardenden, Fife he shared with his mother.
Patel - who gave his job as a medical researcher at Edinburgh University - said he had known Annie "since I can recall.”
He told how his now late father had been the OAP's doctor and that she had become "more friendly" with his family 25 years earlier.
Patel said he would see Annie around once a month.
He then added: "The last time was a week Tuesday past.
"There was an issue with pressure in her boiler. I found out that she did not have cover so I arranged (for a maintenance man) to go out and fix it.
"That was the last time I saw Annie. She did not seem any different to me."
Patel said Annie had been in hospital months earlier, but he did not have any concerns about her health at the time.
The court heard he would carry out other odd jobs for the pensioner including bringing bananas to her.
Officer recalls finding body
It was November 15, 2019 when Patel was arrested on suspicion of murder.
PC Leanne St Aubyn earlier told the trial how she had gone to Annie's home on the day of the alleged killing.
This was to speak to the OAP about her bank account.
The officer recalled: "I continued to knock several times and got no reply.
"I knocked on the front window and could see her.
"Annie was lying in the double bed appearing either deceased or sleeping."
PC St Aubyn alerted other colleagues before the fire service helped gain access through a back door.
She said the OAP was lying in a "natural sleeping position" with covers at her chest, but the officer could not find a pulse.
Prosecutor Alan Cameron asked the constable: "Did you find any sign of injury?"
PC St Aubyn: "No - I noticed her hands were cold to touch, but her chest area was still warm."
Prosecutors claim blunt force trauma was repeatedly inflicted on Annie's head and body.
It is further alleged Patel did "obstruct and constrict" the pensioner's airways by means unknown.
He faces further accusations of theft and fraud in connection with Annie.
He denies the charges.
The trial, before Judge Michael O'Grady QC, continues.