It will ultimately depend on your deductible and the extent of the damage. Unfortunately, backing into a tree will be considered an "at-fault" accident
if you file a claim with your insurance company. Our State of Insurance report
(page 58) shows that at-fault accidents increase rates by about $450/year in Indiana
. Since an accident will impact your rate for 3 years
, you will end up paying around $1,350 in additional premium; not including your deductible. I would recommend getting a repair estimate from a few different shops before you make a decision. If the repair cost is less than the potential increase in your premium plus your deductible, then it's probably best to pay for the repair out of pocket. If the repair costs are significantly higher than that amount, it might be a good idea to file a claim.