In case of a minor accident will my auto insurance rate will be higher?

It depends on what state you live in. In California there is no accident forgiveness like the tv ads show. The bottom of the screens says "not available in all states" or "not available in California.
In California is the damage is under $1,000 and there are no injuries the accident is NOT a point on your DMV record. You might want to post your state.

Depends on the insurance company. Most companies do not raise rates after one accident, although TV advertising makes you think so. It also depends on who was at fault, whether you got a ticket, and the seriousness of the accident.

If the damage was minor and the cost to repair is less than your deductible, or even a bit above, you would be best to simply pay for the repairs yourself and not file a claim with your insurance company.

1

A standard policy across all of the auto insurance companies. They might/may charge you a 10% surcharge for the next 2 to 5 years depending on the ruthlessness of the accident and other options which might be liable to be considered.

Depends. If you have accident forgiveness on your policy, won't be surcharged for this accident, but that only works once.

Or, in some companies, if the damages are w/in a "thresshold" won't ding you. Back in 1996, I rear ended someone and was not charged for the accident. The reason was the other car was old and the damages only cost $300, and since the insurance "thresshold" was $500, was under so not surcharged.

Possibly

If you use your insurance, your rate will probably go up as a result. If you were at fault and your insurance has to pay for someone else's car to be fix, and or if you get a ticket, it will definitely go up. It is just a matter of how much.

It is up to the insurer and your policy terms. Some companies have "accident forgiveness" options (which I believe you pay extra for) which won't bump your rates for that first accident. I have had State Farm for 18+ years without a claim, hit my car door on my garage wall due to inattention, the garage was not damaged but the car door had damage more than my deductible, they paid, and now they are dinging me for 3 years to the tune of 160 per year "accident surcharge". It is all within the terms of my policy, but needless to say I am rewarding that same loyalty with some of my own and shopping the coverage now.

Not necessarily, some companies have accident forgiveness if you have been a loyal customer without being accident prone.

No one here has ESP.

Were you at fault? You didn't say.

If you were at fault, your rate could be higher. Or they could simply refuse to renew you at your next renewal. Or you could have enough safe driver points to offset the accident.