Pay it out of pocket.
The differential is only $1000. That means if your rate goes up by more than $333/yr over 3 years, the insurance claim will have cost you more than paying out of pocket.
You will have an accident on your record for the next 3 years (or is it longer?) if you report it, so rates will go up and so will renewals even at a different company. If you want to know by how much, get a quote from another insurer for research purposes, first with no accident, then with an accident.
Maybe someone with some experience can post how much their rates went up. Generally though for only a grand (because you'd be out the remaining $500 no matter what), I would just suck it up and pay it out of pocket.
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