Three men entered a house in the Bexley area of the town shortly after 10pm on Thursday.
They threatened a 52-year-old man and his 18-year-old son, who were at home at the time.
At around 4am the gang stole the family car, a grey Renault Laguna, changed its plates and drove the teen to a house in west Belfast.
Three hours later, a sum of money was passed to the occupant of the car at a filling station in the Ravenhill Road area in the south of the city. A cash delivery van was in the forecourt at the time.
The car was spotted in the College Square North area before it was found abandoned in Ainsworth Avenue in west Belfast.
The teenager escaped from the house at around 9.30am on Friday and he raised the alarm.
Detective Inspector Chris Wilson said: "This was a horrific ordeal for the father and son and the wider family circle. It was a planned and organised crime involving a number of persons and we are appealing to anyone with information to come forward.
"We need the community to come forward and speak to the investigation team so that those responsible for this can be brought to before the courts."
Police appealed for anyone who saw the car, with either its original plates GJZ 9090, or the false registration number RJZ 6968 to contact them.