The most likley cause of a thumping tire (especially if it has several years on it) is that it is coming apart internally---the belts are coming unstuck from each other, or from the tread. You can often see this on the outside, or feel it by running your hand lightly around the tread. If you don't notice anything, move the car a couple of feet, as the bad spot may be at the bottom.

I am surprised that the car seems to drive OK---usually you will feel vibration in the steering wheel if such a tire is on the front

This is a dangerous condition, as it could let go without warning, though the vibration usually gets worse right before that happens. To be safe, I would replace all of the tires, if the others are the same as the bad one. Though it is possible that the problem is due to having hit a pothole or other road hazard, age alone is likely to be the culprit.

Other possibilities include that the tire in question has worn unevenly and the surface is no longer level---this is known as being lumpy, and is very common on the rear of FWD cars. Did you have the tires rotated recently, bringing a lumpy tire to the front, where it will make itself noticed? If the wheels are locked up and the tires skid for any distance, they can become flat-spotted, which will thump too.