bodypainter

Not necessarily or perhaps not as much. One the things your insurance company will use to calculate your premium is your loss history. In short, the more you cost them, the more they'll want to charge you.

I'm a programmer at an insurance company. What we call Experience Rating uses loss history for the last 3 years. It adds all losses up and then uses that amount to look up a rating factor. If you have zero losses, your rating factor might be less than 1 which will make your premium go down as part of the overall calculation. Losses with make that factor go up and of course when it goes over 1, premiums go up.

Where that factor starts and how fast it goes up depends a little on what state you live in.