Do auto insurance premiums gradually decrease over time?

Reason I'm asking is that I was previously under my fathers insurance as an occasional driver, for about two months but I've since bought my own car and must be listed as a primary driver. My premium for the new car is over $6,000/year, or $500/month - I'm only 18 so that would explain the relatively high rate. If I drive vigilantly and don't get into any accidents, does this rate decrease, even markedly (like ~$10), every month? Or do they remain the same rate for a certain amount of time before you see any decrease whatsoever?

Thanks!

Update:

I'm just wondering whether or not $500/month is too big of a burden to carry on my own if I split from my father's insurance - which of course decides whether or not we finalize the sale on the car.

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