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How to spend less on auto insurance

Many Americans will drive a few miles out of their way to save a couple of cents on a gallon of gas and fastidiously check the air pressure in their tires to improve mileage and save a buck or two. But many fail to take advantage of a simple way to save money: raising the deductible on their car insurance from $500 to $1,000.

Car owners save an average of 9 percent on their premiums by making that change, according to a new report by insuranceQuotes.com. Savings jump an average 16 percent for drivers who change their deductible from $500 to $2,000.

Car insurance deductible
Nick M. Do | Getty Images

The changes do, however, vary by state: Massachusetts gives the biggest break (19 percent) for drivers upping their premium by $500, while Michigan provides the smallest cut (4 percent).

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"It's very interesting to see that in some states raising your deductible gives you a huge savings and in others it barely moves the needle," said Laura Adams, senior analyst at insuranceQuotes.com.

"In some states, you can save hundreds of dollars each year by signing up for a higher deductible, but in others, the reward is so small that it doesn't make sense to risk the higher deductible. This is a good reminder that doing a little research and knowing what's available to you can really pay off in the long run."

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Other states providing decent rate drops include South Dakota at 14 percent, and Kansas, Wyoming and Iowa at 13 percent. Running with Michigan at the bottom of the list are Florida, with just 5 percent savings, and Louisiana, North Carolina and Nevada at 6 percent.

Michigan's ranking isn't much of a surprise given the state has one of the average highest insurance premiums in the country.

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"Michigan is the only state where car insurance includes unlimited personal injury protection," Adams said. "Also, Detroit has a very high percentage of uninsured motorists—as high as 50 percent by some estimates. That unfortunately raises rates for those who do have car insurance."

Detroit drivers pay 165 percent more than the average driver in the U.S.—the highest rate in the nation, according to the website NerdWallet.com.

—By CNBC contributor Mike Strong