Will your insurance go up by a lot if you are found guilty of a car accident? Will it cover your damages too?

YES!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

The front end is designed to absorb the energy of a crash so that you do not. The rear end is designed not to show damage, so it might not show the actual damage. How much your insurance will pay depends upon your deductible. You have to pay first, then the deductible is applied. Talk to your insurance company; you're not going to think your way out of it. Will your premiums go up? Depends on your driving record. Are you a wreckless driver? Have 3 or more tickets? One accident won't raise your premiums.

No, my insurance will not go up.  I have a long history of accident-free driving, and my policy includes rating protection that says my rates will not go up even if I have an at-fault accident.  (But no promises if I have a second one)

My insurance policy will fix my vehicle if the accident is my fault, because I have Collision coverage on my car.  I pay the $500 deductible, and my policy pays the rest.

But that's me and my policy.  Do you have rating protection?  Do you have Collision coverage?  You didn't mention either of those, and they really matter.

And you'll be found liable, not guilty.  Liable means legally responsible for the damage, and there is no way you won't be held responsible.  Rear-end collisions are always the fault of whoever did the rear-ending, no exceptions, and you did the rear-ending in this one.  Even if the other guy jumped on the brakes for no reason at all, it's still your fault.  Your insurance company has already accepted 100% liability on your behalf, in fact.  Yes they're allowed to do that, it says so right in the contract.

Ok so. YOU, not him should notify *YOUR* insurance.  Ok so, Your insurance may go up because of this and it may not go up.  Ok so, You have no control over that.  Ok so You have insurance for just such a thing.....USE IT ! Ok so.

Ok so, by the way, according to the picture  your car was not "destroyed" it merely has some front end damage.   Ok so ?Why would anyone begin a question with "OK SO" ?

Grammar matters

If you have only liability or you have only comprehensive and collision, then it will not pay for your damages. If you have collision coverage or full coverage, then it will pay for your damages, minus the deductible.

I can't tell you what to do with your insurance you really ought to talk to a lawyer first but I've got some good news for you if that's your blue car there with the caved-in bumper you can fix it yourself in about 15 minutes take the wheel off support it with a cinder block and a jack and get yourself a heat gun at harbor freight about $15 get yourself a two by four and a rubber hammer. From the other inside heat up the caved in area well don't burn it keep moving your heat gun around and around and around. About 4 minutes round and round. Take your two by four and your rubber hammer and give it a tap it'll pop right out. Continue heating and pushing it back into shape with the handle of your Hammer until it looks right then let it cool. Most of the time it doesn't even make the paint fall off. Body shop told me $800. It costed me less than $20 and you can't even tell it happened!

Whether you call or not is irrelevant. Stupid people don't return calls from their insurance agent. 

Yes, it's expensive and dangerous to tailgate another car.

If you have collision insurance, they will pay for your car. If you don't, they won't. Of course he will claim against your insurance, not his since it was your fault. Your rates may or may not go up based on your history on the policy and driving record.

It depends on your insurance policy. Some people only have 3rd party insurance, which pays for the damage to other people's property, but not the owner's. 

Full coverage insurance will cover the damages to your car (after deductibles). 

Will your insurance go up? Probably -- people who have one accident are statistically more likely to have more accidents, so the risk is considered increased. But the damage in the picture doesn't look like "destroyed", so it probably won't be a major increase, whereas a write off would,