While taking reverse my car hit another car. First I thought I can pay from my pocket as it was a small dent but she says it cost around 2800$ I wants to know will the Insurance company going to charge my premium huge in future claims?

They might. You don't say where you live. Also was this in a parking lot or street. Do you have safe driver credits where you are.
$2800 sounds very high for a bumper. What exactly did you damage?

Depends on your insurance company. When did this accident happen? If you do not report it within the insurance company's guidelines they may not pay.

It happened at Columbus private parking lot. I have safe driver credits and never did any accidents before. I have not reported to insurance yet thought it was small dent can be paid out of pocket. My question is whether my insurance will increase my monthly premiums in future.

... My quesion is whether my insurance will increase my monthly premiums in future.

Possibly. Why not ask them, anonymously?

If you have a good safety record it may not happen. Also, did you see the estimate? The other driver may be lying about the amount. If you report it, she will have to go to your carrier to have the damage assessed.

So report it today.

If you have discount for safe driver now you will lose those, so it will go up, and may even go up rated for one accident. Have you asked the other driver for two written estimates that you would pay by ?

Again - depends on the carrier. We lost the safe driver's discount when my husband's vehicle was struck in a parking lot - and there is no question that he wasn't in it, had nothing to do with the hit and run. And that was a claim on our collision coverage!