You are not responsible for a deductible
unless you have comprehensive
coverage. Since you only have liability
, the damages to your car will not be covered which means there is no deductible
. Keep in mind, an at-fault accident raised rates $468 per year in Illinois in 2018. Over a 3 year period, which you will typically be charged for after a violation, that $468 stretches to $2,524. If you're able to, it might make sense to pay for the other driver's damage out of pocket. Keep in mind, the other driver is under no obligation to accept your offer. But it can be an alternative to the rate increase. For more information regarding filing a claim, see here.
Good luck and if you have any questions, don't hesitate to ask