You have to look at it in a few different scenarios. First off the car is only worth about $1500. Is it really a smart investment to dump $6200 into a car worth so little? You could take that $6200, along with whatever you may get out of the Volvo and buy a newer car, but you may get a car with a checkered past.
I took the second option myself. The transmission did go out on my 07 Grand Prix, and rather than waste time and money on a car worth so little I bought myself a newer car that gets better fuel mileage. I hate having a car payment again, but I have almost no worries about this car. My Pontiac had me nervous for years, because of the notoriousness of the transmissions randomly failing.