I would recommend having it inspected by a dealership with a volt technician. In most cases, it should receive a clean bill of health, but a certified tech will definitely know what to look for if anything is askew. If possible, find out if seller has service records. Maintenance should be minimal due to the nature of the car, but I would like to see at least a couple oil changes having been done as well as any other required service by mileage as noted in the service manual which can be found with a simple search on here, or google. Aside from the basics, I can't think of much that may be checked on the car as the general consensus that I've come to find is that they've really over engineered this car and problems should be pretty minimal. If you get a chance to check out the energy usage screen, there will be a figure that shows the vehicles lifetime mpg, The higher that number is, the less the engine was utilized which is a plus, but even a low number such as 35 mpg is not really a reason to worry since the engine really only powers a generator the majority of the time, so work load and wear/tear isn't as high as a traditional ICE vehicle. All in all, if it's a vehicle you can see yourself driving regular, has the options/color you want (or are ok with) and the price is reasonable, there really is no reason not to seriously consider having it checked out and going for it.
I found a 2012 Volt Base Model at $14,500 on cars.com, so I am guessing that you are limiting your expenditure to that price point. If you can finance a bit more, you could have a Certified Used 2015 Volt Base Model with 20,000 miles for $20,000. I found a Certified Used 2016 Volt Base Model with 20,000 miles for less than $23,000. Suggestion: Consider financing an additional $10,000 for the greater range and other advances in the Generation Two 2016 Volt or delay your purchase for a few years until the prices drop on the Generation Two vehicles. If you are faced with urgency and limited budget, then go ahead with your plan. I own the 2013 Volt Premium Model that I bought at $20,000. I may upgrade to a used Generation Two in 2020. However, I suspect that there will be a better hybrid available, more versatile in utility, in four years that may tempt me.
If you're in an area of the country that gets cold, make sure your Volt has factory heated seats installed, since you'll get better range using the heated seats than heating the cabin. Aftermarket heated seats will probably require disabling the airbag sensor, which is why you want factory.
2013 and above Volts have "Hold" mode, which allows you to switch to CS (gas) mode at any time. CS mode is more efficient for highway and EV is more efficient for city use. Hold mode lets you save your battery for driving around town at your destination.
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