AS with most types of insurance, you can lower the monthly premium on your homeowner’s policy by raising your deductible. But whether it makes sense to do so can vary by state, a new report finds.

The deductible is the amount of a loss you must cover out of pocket. Deductibles for homeowners’ policies typically range from $500 to $1,000, but may be as low as $250 or as high as $5,000. The average annual premium, meanwhile, was $1,034 in 2012, the latest data available, according to the National Association of Insurance Commissioners.

An analysis done for insuranceQuotes.com, an online insurance site, found that raising a homeowner’s insurance deductible to $2,000 from $500 lowers the average annual premium by 16 percent nationally.

The potential savings, however, are much larger in some states, the study found. In North Carolina, for instance, a similar increase in the deductible saves homeowners 41 percent, while homeowners in Rhode Island, Florida, Connecticut, Pennsylvania and Massachusetts would save 20 percent or more.