The math does not lie. You may also consider buying an even older, lower cost car if you can find the right deal.
Depending on your state, you may also need to include sales tax in your used car purchase, which won't change your math very much.
Once you add in the cost of gas over that decade (probably 5,000 gallons for 150k of driving at 30 mpg) yo end up saving about 10% or so by making the change. You can use the money you saved to buy a bike, drive less and save even more as gas will be about half the cost of ownership over that decade.