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The mistake doubling your auto insurance premiums

When was the last time you shopped for auto insurance? There's a good chance you're overpaying.

Insurance experts typically recommend shopping for a new policy every year or so—and maybe more frequently if you see a big rate jump when it's up for renewal. But few people do.

A 2012 Deloitte survey found that 24 percent of people "never" shop for insurance alternatives, and another 34 percent "rarely" do. Only 18 percent shop their policy annually.

"We have a combination of fear and boredom," said J. Robert Hunter, director of insurance for the Consumer Federation of America. Shoppers recognize the importance of shopping around, but it can be a daunting task.

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That inertia is expensive, however. Prices can vary by more than 100 percent from one company to the next, said Hunter. Savings can run several hundred dollars—or more. A CFA study released Monday found that in 9 percent of 1,377 lower-income ZIP codes studied, the average premium quoted for the minimum, state-required coverage was $2,000 or more. But in 14 percent of zip codes, at least one insurer quoted a price above $3,000.

The average policyholder is overpaying by $368 a year, according to a 2013 NerdWallet.com study. (See chart below for some of the most and least expensive metro areas, by average insurance rate.)

Most and least expensive cities for car insurance

Metro area
Compared to $797 national average
Detroit-Warren-Ann Arbor, MI 165% higher
New York-Newark, NY-NJ-CT-PA 36% higher
Miami-Fort Lauderdale-Port St. Lucie, FL 34% higher
Los Angeles-Long Beach, CA 25% higher
Atlanta-Athens, GA 17% higher
Chicago-Naperville, IL-IN-WI 16% lower
St. Louis-St. Charles-Farmington, MO-IL 18% lower
Pittsburgh-New Castle-Weirton, Pa-OH-WV 24% lower
Cleveland-Akron-Canton, OH 31% lower
Charlotte-Concord, NC-SC 43% lower
SOURCE: InsuranceQuotes.com.

To make shopping around easier, start by visiting the web site of your state insurance commissioner. They often have consumer guides to finding a good policy, as well details on typical pricing and complaints for individual insurers, said Hunter. That can help you narrow a search down to three well-reviewed companies with good rates, to follow up with for a more detailed quote.

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Be sure to let your current insurer know you're shopping around, too. "They may have options to put you into lower prices," he said.

—By CNBC's Kelli B. Grant