Cars - Pay Cash or Finance & Invest?

[Colin Smith]

My wife has finally ran her 1999 Volvo into the ground with the transmission going out and it would cost more to fix it than the car is worth at this point in time. 

Let's be clear that we are looking to buy a 3+ year old USED vehicle, looking to spend about $10,000. New vehicles are not part of this discussion as we have no interest in losing ~38% of the cars value in 3 years due to depreciation.

With auto loans being so low for used vehicles (~3%), it makes it hard to pass up, however, there is something to be said for owning your vehicles free and clear, as we do now. 

The questions is, would you pay cash and own your car free and clear, or would you finance the vehicle and invest the cash into RE?