Your analysis misses three critical elements.

• When you buy a home with a mortgage, you're leveraging your investment, typically 5-fold (assuming you pay 20% down). Historically, residential real estate in the US has appreciated about 4%/year. Your typical appreciation would thus be about 20%/year on your invested capital. After correcting for the historic average of 3% inflation, that return is still about 17%.

Why You Should Consider Real Estate Investing

• When you take out a mortgage, the principal part of your payment isn’t a cost of the mortgage, it’s the purchase price of the home, unevenly divided over the life of the loan. Your real financing cost is your interest rate, less your tax benefit, adjusted for inflation. If your interest is 4%, your combined marginal tax bracket (federal, state, and local) about 30%, and inflation is running about 2%, your cost is just under 0.8% ((1+0.04*.7)/1.02). If inflation starts running higher, your real financing cost may turn negative — i.e. you start earning money on your mortgage!

Why Prepaying Your Home Mortgage Is Almost Always a Terrible Idea

• Assessing the purchase of a home by itself is meaningless. You have to compare it to the alternative housing solution you’d have to go with — renting. The data show that while home-ownership is expensive, the cost of renting a comparable home is far more expensive.

Here’s Why You Shouldn’t Be Renting Your Home (and When You Should Anyway)