Should I report a minor accident to my insurance company?

Based on what you included, you most likely should not report it to your insurance company. Your insurance rates will in all likelihood go up over the course of the next three years more than $600 to $700 so financially it's not a good idea.

First, though, you don't have a deductible for the damage you caused to the other car. There is no deductible when it comes to liability. Any deductible is for damage to your own vehicle, including both comprehensive and collision coverage. If you need to fix damage to your own car due to backing into something than your collision deductible would apply.

You should also know that if you even ask about this with your insurer they can and probably will increase your insurance premium even if you don't file a claim. By calling them you make them aware of the accident even if you don't file a claim and they don't pay out on it.

A good rule of thumb is that an insurance claim should be around two and a half times the deductible that you have to pay if a deductible applies. I really don't think this is the case at all if you just caused $600 to $700 in damage. $500 is your stated deductible and is what the average driver carries on both comprehensive and collision.

If you use an independent insurance broker it is usually safer to call them for advice about a car accident. They are typically less likely report it to the insurance company after they finish talking with you. If you call an insurance agent that is a captive agent, in other words can only sell that insurance company's policies (State Farm, Allstate, Geico, etc.), it's a lot more likely they'll report the accident to the insurance company and your rates will go up even if you don't file the claim.