There are some companies that offer reasonably affordable premiums for teenagers like cheap insurance for young drivers. Will most people think of these as cheap rates? Probably not, but it is possible to locate some decent discounts through a little research and effort. Paying auto insurance for a teenager driver can be expensive; any little bit of savings is most certainly worth it! When you do your due diligence online and research auto rates, you may discover that there are widely differing rates for similar age teenagers from different insurance carriers.. There are a variety of factors that will determine your premium cost.