Be sure to check out the deals available from local small banks and credit unions. Many small banks and credit unions send refinancing solicitations to recent car buyers. These offers may turn up in your mailbox just a few weeks after you've purchased a car. So be on the lookout.

Loan and title fees can eat into your expected savings. Ask the lender for a breakdown of these charges when shopping for your loan. You can also use Bankrate's auto loan calculator to compare the new payment with your current payment.

If you owe more than the car is worth

If you are having trouble making your payments, the best alternative is to talk to your current lender about extending the term of your existing loan. They won't want to do it, but if you can show them why this is important to keep you solvent, they should grasp that it's better to restructure the loan than have you default.

Dangers to refinancing your car loan

• Are you currently in the market for a mortgage loan or other secured credit? If so, postpone the auto refinance. A loan application and approval will show up on your credit history and will have a negative short-term effect on your credit score.
• Refinancing an auto loan often means trading a new-car loan rate for a less-favorable used-car loan rate. This difference may offset some of the benefit of lower interest rates from the borrower's perspective.
• Avoid loans with prepayment penalties or where the interest is not computed on a simple interest basis. You want to have the ability to pay off your loan faster if you are able later down the road. Make sure this is possible -- that you only pay interest for the time the money is borrowed.
• Be wary of attempts by the lender or your own temptation to stretch the term of the loan. Make sure you aren't trading a lower monthly rate for a larger total loan.
• Before agreeing to a refinance, do the math and make certain you are actually saving money.

Don Taylor, Lucy Lazarony and Amy Fleitas contributed to this story.