Teens are insanely expensive...about $1,000 each here in the Philly Burbs, and that's for kids with good grades. We learned the hard way that you have to get insurance for them as soon as they get their license, whether they drive the car or not! Eldest is in college 13 hours away, home for maybe 3 months a year if he works summer here and not elsewhere, so they are "generous" and give us a $200 break for him.
Philly is crazy expensive for insurance anyway. I would tell you what we pay for that, but it would depress me to look it up. Can't wait to downsize and leave this high COL.
Hand your teen cash for a taxi for every trip. Sounds like it would be cheaper! Definitely safer for your kid.