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A mortgage isn't a cost. It's an investment. You would call money you put in a 401k a cost either.

Where do you live if you take the money out of the house for retirement? In a practical sense, it’s a cost.

If you move to a much lower cost of living area, then the difference in expenses is the return on investment.

The point is home equity is value you own. You can get money out a lot of ways: relocating, downsizing, reverse mortgage.

With rent you are out on your ass with nothing the moment you stop paying.