For a better auto insurance rate, just ask

Cutting your auto insurance bill might be as simple as asking if you qualify for a better deal.

Just 16 percent of consumers have asked their auto insurer for common breaks like low-mileage rates or good-student discounts, according to a new InsuranceQuotes.com survey of 1,000 adults. "The first issue is awareness," said Laura Adams, senior analyst for the site. "A lot of consumers just don't realize that discounts are available. They think the rate is the rate, and there's no way to move off that."

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That's a mistake that can leave big money on the table. In California, for example, where the average insurance premium is $750, someone who gets a low mileage discount for driving 5,000 miles per year instead of the average 15,000 could save as much as 25 percent, according to InsuranceQuotes.com data. "Any time you can go back to your carrier and say, 'I'm driving fewer miles, please re-rate me,' it's worth it," said Adams. A married 20-year-old could pay up to 21 percent less than a single person of the same age, for example, but the survey found that only 13 percent of the adults had alerted their insurer after they tied the knot.

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The fix is simple: "Ask what discounts are available, and ask regularly," said Amy Danise, an insurance expert with NerdWallet.com. Discounts vary by insurance carrier and state, but an agent should be able to walk you through which are available. Alert your agent when you have a life change—be it a move, a new job or a family shift—that could benefit your rate. And keep the potential for discounts in mind when shopping competitors for a new rate, Adams said. Initial quotes may not account for discount-qualifying details like whether you've taken a defensive driving class or if you're an A+ student.

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Chasing discounts won't always improve your bottom line. "In urban areas, rates are usually much higher because vandalism is up, and theft and accidents," said Loretta Worters, a vice president for the Insurance Information Institute, an industry group. Plenty of insurers will offer you a break for parking in a garage instead of on the street, she said, because that reduces your risk. But the cost may more than offset any deals: Median monthly parking rates in major cities range from $55 per month in Phoenix to $562 in midtown New York City, according to a 2012 Colliers International study.

The biggest dent in your rate that you can make is to be a safe driver. One $2,000 property damage claim can hike rates an average 41 percent when it's time to renew your policy, according to a January InsuranceQuotes.com study. That's more than enough to counterbalance any discounts on your record, said Danise—and of course, it's a safe bet any "safe driver" deals will also disappear.