Diapositivo, your calculations are ignoring a very large factor - risk.

The purchase of a home hedges the risk (borne by a renter) of rising home values and hence, rising rent. There is value in having one's housing expenses relatively fixed for a number of years, as provided by a mortgage. Further, in assuming your investments will be profitable, you also dismiss the risk of your skill in choosing investments that will (as you do recognize in the case of land) go up, down, or stay the same.

There is another thing to be said for real estate - they ain't making any more of it.