Consumer Reports and the like have calculated "true cost of ownership" for different model cars you can use as a rough guideline. They estimate depreciation, taxes, financing, gas, maintenance, and insurance over 5 years. However, that's just a rough estimate and only a first step, it doesn't take into consideration individual variables. If you are a young male, have to drive in stop-and-go traffic every day, and pay to park everywhere your cost of ownership will probably be close to double.
Auto insurance alone is probably close to $100 a month for the average American - depending on your car, location, and driving record, of course, I'm just making an educated guess. IIRC, last I ran the numbers with my car (average budget model) cost of ownership was around ~$20,000 over 5 years. That's amortized to $333 a month.
The main (and perhaps only) advantage to having a car is the convenience and the ability to go where ever whenever.
But it's certainly true that for people who don't need to drive on a regular basis, a lot of reason to own a car may come down to things like not wanting to deal with Zipcar or a regular rental car every time you want to do a big shopping trip or get out of town on a Saturday or for the weekend.
For example if you have a friend who lives 15 miles away - it becomes "do I want to spend $50 to visit my friend?". If you drive your own car, the economic calculation is invisible - it's about $2 of gas, a bit of depreciation that you don't even think about, and [huge already-paid upfront cost for vehicle/financing/insurance that you don't even think about] - "of course I'll pay $2 to visit my friend!"
One thing that helped was making a spreadsheet that showed how my total cost of transportation went from $8k/year to about $1200/year when I switched to Lyft/ZipCar and ditched my own vehicle. So even if I were to add in a weekly $50 friend-visit, I'm still paying less than half for my transportation than I previously was.
Some might say this was a good thing. Personally, I think mobility is generally positive.
As it should, as well as an environmental consideration.
-- Amount that you drive
-- Availability of Uber when/where you need it
-- Whether you have to pay for parking
-- Whether you also take a lot of weekend trips
-- etc.
$100 per month is actually not very much. That suggests you're only traveling 100 miles per month or so on Ubers which is nothing. By contrast, that would basically take me to the nearest large city and back once or get me back and forth to my office a couple of times.
If you live in a city, you'd probably pay a pretty decent chunk of that amount just in auto insurance.
If you go for a new car, you could easily pay $600/month - at that point it would take > 18 years to break even.
Of course, there are other things to take into account: convenience on the one hand, maintenance, parking, & insurance on the other.
But, my gut instinct is that you'd be better off to keep taking uber and invest the difference in an index fund. Keep that up for long enough and you can buy a new car in cash (or retire early).
[edit]: Don't forget that you can bicycle also. A $400 bicycle has an incredibly high ROI if you replace a few regular car trips with bicycling. It's a net gain for your health too! (You may already be doing this, but it's worth pointing out anyways ;)
Do those numbers include maintenance and insurance? IME just routine maintenance on an oldish (60-100k) Toyota runs into the hundreds of dollars. Insurance again something like ~$800-1000.
I got rid of my car after I did the math and realized I was spending $1500-2000 a year on just insurance and maintenance.
My wife and I have never had any significant trouble (tickets/accidents/etc.) though, and it was collision insurance only. We also don't drive much. (I bike into work or else work from home.)
(Collision = cover other people's bills when you cause an accident. Comprehensive also fixes/replaces your car if it's wrecked, but that doesn't really make sense on a 10+ year old car.)
We also have home and life insurance through State Farm, so there may be some bundle discount going on.
My specifics: I live in Cupertino and work at home. I have a wife and kids. About four times a month we have a situation where we need two cars, because one of us has to be somewhere other than where they kids need to be.
Unfortunately, most of the time that's San Francisco, which is about $80 round trip with Uber/Lyft. I could sometimes use public transit, but usually the times don't work out and it takes a really long time, and I'd still need a ride to and from the train on both ends.
I have a five year old car so the payments and maintenance still come out to a little be less than Uber/Lyft, and since I've already got another car, the cost of insurance doesn't add much.
It's pretty close in cost, and the convince pushes it over the breakeven point.
12 trips a month makes the calculus easy: don't buy a car.
Additionally, if there is frequent and reliable train or bus service to your destination that may be a better option than driving. I know several people who don't own cars but travel 100+ miles via bus on a regular basis. On the other hand, I travel 100+ miles regularly but buses and trains don't go to where I am going.
(There's people who justify buying a truck because they need to haul stuff twice a year at the most. Renting a truck twice a year is almost guaranteed to be a better option financially. That being said, if you want a truck because you like trucks, that's also a perfectly valid reason to buy one.)