Yes, age of car affects insurance because insurers take specific vehicle details into account when determining car insurance prices. For instance, a 10-year-old version of the same car will cost less to insure than the brand-new model, since it is less valuable.
Similarly, valuable cars, high-performance models, and cars that are more likely to be stolen will usually cost more to insure. Cars with high repair costs, added features, and poor safety records can also raise premiums.
Since your car's year, make, and model will affect your insurance premium, it's important to check quotes before you purchase a new car so that you'll know how much to budget for insurance. For more information, check out WalletHub's guides to the factors that affect car insurance rates and the cheapest cars to insure.