Based on the information you've provided, I'd suggest you don't replace your car at all. Today's cars should be relatively trouble-free for at least 100,000 miles, and you're not even halfway there yet.
Assuming you're not having any extensive problems with your car, you'd be much better off saving yourself the monthly payment on a car loan or lease as well as the increased costs in car insurance because you'd be driving a new model.
Just be sure to keep up with the car maintenance schedule as recommended in the owner's manual, and you'll save yourself a lot of money. If you're concerned about your car being out of its new car warranty, consider adding mechanical breakdown insurance to your car insurance policy to provide you some reassurance in the event of a breakdown.
That said, if you feel you must replace your current car with a new car, buying a new car outright if you can afford it would be the smartest financial choice. You'll save yourself the interest if you had a car loan, and you will actually own an item that is likely to be a substantial asset, especially since you drive so few miles. In addition, should you die, owning the car outright will be easier on your heirs. They could be liable for payments on the remainder of the lease or car loan, depending on the contract and the laws in your state.
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