I'm entering the hot debate of rent vs buy with what seems to me an overlooked factor in every thing I've read: If you rent you're giving money away. If you own you have an asset to sell.
You're still giving a lot of money away when you own.
Let's say you can rent a 172 for your private and instrument for $125/hr, an Arrow for $150/hr, and an instructor for $50/hr. Let's say you use the 172 for 240 hours and the Arrow for 10, and the instructor for 80 (30 private, 40 instrument, 10 commercial). You're looking at a total bill of $35,500 to get your hours and ratings.
Now, let's look at ownership. You still need the $4,000 for the instructor. You buy a 172N for $40K, fly it for 240 hours. It'll depreciate in value by about $20/hr just for the engine and airframe time, so let's say you can sell it for $35K. I'm going to suggest you still rent the Arrow, it isn't worth buying a plane with all the associated one-time costs for 10 hours.
Now, let's look at the additional costs. I'll use what they are in my area. Your results will vary.
One time: ($13K)
* Pre-buy inspection, escrow, title search, etc $1,500
* Sales Tax $2,200
* Depreciation $5,000
* CFI is still gonna cost $4,000 if you're lucky, many FBOs charge more for CFIs when not instructing in their planes.
* Arrow rental still $1500
* Registration fee(s) $250
Annually: ($3K/$2.5K)
* Annual Inspection $1500
* Insurance $1500 first year, $1000 thereafter
Monthly: ($3K/yr)
* Hangar rent $250/mo
Hourly: ($90)
* Gas $40/hr
* Maintenance $50/hr
So, if you actually keep the thing for 5 years and 250 hours, you will have spent around $68,000 instead of that $35,500 you spent renting.
If you're a little more motivated and can do all your hours and ratings in one year, it'll still cost $41,500 instead of $35,500.
Also, this is essentially the best-case scenario. What if you buy the airplane with a mid-time engine, and then the engine throws a rod? Now you're on the hook for a $22,000 overhaul plus around $6,000 for removal and reinstallation. You'll get about $11,000 back in added value when you sell the plane (assuming you bought it priced accordingly with a mid-time engine) but that's another $17,000 down the tubes. Did you happen to have $28,000 lying around?
Now, if you're still going to do this, here's how to maximize your chances of not losing money:
1) Pay cash for the plane, and have enough left over to pay for that $28K overhaul should it happen. That won't save you anything over what I've outlined above, but it will mean you don't have any added interest expense, you just have the lost opportunity cost.
2) Fly at least once a week, or more often. That will help keep your maintenance costs from getting any higher. Again, my numbers above assume this.
3) Do as much of your own wrenching as you can: Find an A&P mechanic that will let you do the work yourself and sign it off. You could potentially save up to half of the maintenance costs this way.
4) Since you're just building time, make sure that you find the cheapest gas in your area, and make that a frequent stop.
5) Find a partner. This is a great way to cut your fixed costs in half.
6) Find a flying buddy to split the hourly costs with - Best scenario here is for this to be your partner as well so you can swap back and forth and split safety pilot time.
It's hard to financially justify owning an airplane, ever. The justification comes from being able to go on short notice, to have it available all the time, to fly a nicer airplane than you'd be able to rent, or even just pride of ownership. I can make individual trips look good on paper when I do a business trip, but that doesn't really include any of the expense of owning the thing in the first place.
So, do what you want to do - Just don't expect it to save you money.