You truly could be saving $400 a year on car insurance

From the GEICO gecko to Progressive's Flo, TV ads for car insurance constantly nag you about saving by comparing rates. But more than one-third of car owners apparently aren't listening, according to a new study by personal finance site NerdWallet.

A survey shows that 17 percent of car owners with insurance have never compared rates, and 21 percent haven't done so for at least the past three years. If you're among that 38 percent, you could be missing out on an average of $417 a year in savings, NerdWallet calculated.

The online survey of 2,072 people also showed that more than a quarter (28 percent) of respondents think they pay too much for their insurance. Among millennials (age 18 to 34), that number rose to 33 percent.

To find out if you're overpaying, go to this NerdWallet calculator. Put in your zip code , and it will show you how much savings you may be missing out on. . It shows you your lowest quoted rate based on the information you provide and compares quotes from major insurers 

Remember, today's auto insurance rates are set by a complicated mix of your driving history, what car you drive, where you live and your credit rating. So over time you may be able to cut your insurance rates by, say, improving your credit rating.

In the meantime, compare rates for your current situation. "It's good to price-check your car insurance regularly because rates change all the time," said Amy Danise, insurance analyst at NerdWallet. "The insurer who gave you a good deal three or four years ago may no longer be among the cheapest options." She suggested comparing rates in these cases:

• When your policy is renewed, often annually. Insurers typically raise rates upon renewal.
  
• When you add another vehicle to your policy or another driver. If that driver is a teenager, your rates are sure to go up. That makes it especially useful to shop around.
  
• If you have a major life change. That is, if you get married, switch jobs, retire or move to a different ZIP code.
  

In another part of the survey, 10 percent of respondents admitted that they had intentionally lied to insurers about their personal or vehicle information when buying a new policy. That included reporting lower mileage than the car actually has, leaving a driver off the policy or saying the car was garaged when it's really parked on the street.

In this digital age, insurers can discover almost any detail about your life. As NerdWallet cautions: "Misleading insurers can backfire. If you get into an accident, and your insurer discovers your application had false information, the company could deny your claim."