Here is another way to think about this that takes all the complicated calculations out of the way. When you rent, the owner has all the costs involved that you would if you owned the house. The rent he charges you will recoup ALL his costs PLUS he will want to make a profit, let's say 5%. Your extra cost while renting is his profit margin. This extra cost is money that you cannot invest in your 9.5% return investment. You are paying a "middle man" and that always adds expense; to you.
For argument, lets accept rent on a single family, 2 bedroom home worth $300,000 is $2500/month. At a 5% markup, you are paying ~$125/mo./$1500/yr. profit to your landlord, money that as an owner you would NOT have to pay. You would also lose $142.50 (9.5%) on not being able to invest this money = $1642.50 lost per year x 30 years (life of a mortgage) = $49,275 lost at the end of 30 years. This ignores compounding effects so it's really far worse than that, a quick spreadsheet calc for compound losses came up with $120,000 after 30 years. PLUS, at the end you have no asset while the owner has a $300,000+ value escalated asset. PLUS+, the above treats rent as fixed while it certainly will NOT be vs. the owner has a fixed, predictable mortgage. PLUS++ at the end of 30 years if you rent, you would still be paying an ever increasing rent while if you owned, your mortgage would be paid off. That's a nice perk as you head toward retirement and a decreased income.
I don't care how you work your numbers. If you come to the conclusion that paying a middle man landlord will be cheaper than owning yourself and building an asset in value, you are missing something BIG. Your rental costs will be the same as his PLUS his profit. Your rent also gains you NOTHING permanent while it funds paying off his mortgage and building his asset value which is also increasing due to inflation. He meanwhile gets to charge you inflating rent prices.
Oh, BTW, when you get around to selling your house (primary residence), you can write off $250,000 ($500,000 joint return) of capital gain on your federal taxes. Try THAT with your 9.5% investment.
FURTHER, you can do this every 2 years. Over time, you could shelter $$millions of home value growth from capital gains taxes. $2 million sheltered @22% tax (or more) would save you $440,000. Project that back 30 years and it is worth almost $15,000 per year! As a renter, you get ZIP when you change apartments.