All other things being equal, it may cost more, yes.
However, what the insurnace companies in my experience are more interested in are the following: The Age of the Roof, The Age of the plumbing and what type, The age of the Furnace and Air, the age and type of the electrical. For many of these its more a question of when was the last time these items were brough up to code, either partially or fully. Obviously there are many many more underwriting criteria.
Another consideration that I have noticed is that some carriers general underwriting guidelines will not allow then to write certain age homes. Typically you can start seeing this at about 1930s homes and earlier. So if you have a home that was built in 1920 will have far fewer insurers bidding on your home.
I hope this helps.
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