The math is going to depend on what you buy. If you get a 35
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.
An example, say you're going to spend $20k (airplane rental only; instruction fees excluded from this example) on getting your Instrument and Commercial ratings and it will take you 5 years. If you rent you've just given away $20k. If you own you have an asset at the end of your training that you can sell. Even if ownership costs such as gas, insurance, maintenance, tie downs, etc. are $15k over 5 years you are still $5k ahead assuming the plane holds it value. Even if it loses $3-4k in value you're still ahead. If you get a mogas STC'd 150 certified ifr trainer, follow Mike Busch's maintenance advice, do all the things you can yourself, tie down at a cheap airport, you might spend a lot less than $15k over that time and come away with even more.
I'm ready, tear my assumptions apart!
The math is going to depend on what you buy and that's true whether it's a house, airplane or wife.
But the major assumption you're missing is maintenance and the real fixed vs variable costs. You made an assumption of $250/month for gas, insurance, maintenance, tie downs, etc....and that's way too low. First of all, gas and maintenance are variable cost, not an ownership cost. Whether or not $250 is reasonable in your part of the country is entirely up in the air. Here, flying a beat up old straight wing Warrior, $200 is about the right monthly price for insurance and a tie down at the county airport closest to me. All I get to do for that price is park it outside and hope we don't get a hail storm. There's no hanger, that would take this up to $400/month for insurance and a hanger.
I go back and forth with whether or not to include a purchase price. Financial types talk about opportunity cost of money, but the truth is, nobody really cares to track that because it's all a hypothetical cost and you never know the opportunity cost until well after the opportunity. I'm going to do something with that money and I could park it in stocks, bonds or precious metals just as well as buying an airplane. However, if I'm financing an airplane, then it is money that I have to spend every month so it has to go into the cost. Say $400/month for a loan payment. Yes, at some point the airplane will be sold for some value, but if I do this right, it will be my estate that sells it, so I don't really care what that value is. Of if I really, really do it right, my son will take the plane and it will be his estate that sells it in which case I really, really don't care.
Now you have to figure your variable price - how much do you need to pay and to save for hourly operations and to pay for future maintenance.
Fuel - 8.5 gph x $3.80/gal gives me just about $40/hour for gas.
Engine rebuilds are standard at $11/hour FOR A NEW ENGINE. This varies by the airplane, but typically I use a formula to calculate how much I need to put into the engine fund to pay for a future overhaul and that formula is ($22,000-kick start) / (TBO - SMOH). The kick start is how much I put into the engine fund to start it off. This allows me to save less per hour if I'm considering a high time engine, but it also makes high time engines very unattractive (sellers take note). For an example, take an airplane which has a TBO of 2000 and 500 hrs SMOH. I will put nothing into the kitty when buying the plane. That's 22k/1500 hours remaining on the engine or $14.67 to be saved every hour that I fly, call it $15.
Similar, I put aside for maintenance, but how much is a guess. I go high on this and call it $30 hour for maintenance. Maybe it's only $15, but I'd rather be surprised than shocked.
So, variable costs for my calculations are $85/hour flown and $600/month have the airplane on the ramp. Where is the break even on that? For me, it comes at about 15 hours a month flying, with an hourly cost of $118/hour. If I don't include a loan cost, then break even is at 3 hours with an hourly cost of $126. If you're wondering why the break even changes, there is a monthly fixed cost for club dues that gets amortized over hours flown...that changes the effect rate for the club.
The other important number is how much are you actually spending. At 15 hours and $118/hour, it's $1655 per month. Can I afford to spend that? Sometimes, yes. Sometimes no. Therefore I don't have a plane.
The club I belong to is a true club, not for profit. But they do have pretty substantial overhead in terms of building and operations that I don't have, so I think my numbers are probably pretty close to the mark. One of these days I'm going to have to prove them...