There's not a single answer here, as the premium you pay for car insurance depends on multiple factors, including (but not limited to):
- driving record
- Demographics (gender, age, etc.)
- type of car (sports car, sedan, SUV, etc.)
- Driving habits (how long, how often)
- Amount of deductible
All these factors contribute to the likelihood of getting into an accident, and the expected damage from an accident.
So just having an accident and making a claim will likely raise your premium (all else being equal), but whether or not it will be cheaper in the long run depends (obviously) on how much your premium goes up, which cannot determined without all of the facts. Your agent could tell you how much it would go up, but even making such an inquiry would likely be noted on your insurance record, and may cause your premium to go up (although probably not by as much).
However, the point of insurance is to reduce the out-of-pocket expenses from future accidents, so the question to ask is: How likely am I to have another accident, and if I do, can I pay cash for it or will I need to offset some cost with an insurance claim. Do you risk making a claim and having your rates go up by more than $700 over the next 3-4 years (the rough time it takes for a "surcharge" to expire)? Or do you just pay for the repair out-of-pocket and keep your premiums lower?