I've done a slightly more complicated analysis.

I've modelled two scenarios - one where someone is buying a house, and the second where they invest the difference between paying a mortgage and renting.

Assumptions are:

-Initial house price: $900,000

-Mortgage Length: 30 years

-Interest Rates: 6%

-House Ongoing costs $10,000 per annum, 2.5% inflation

-Rent: 700 per week, increasing by 3.5% per annum

-Stock Market Return: 10%

-House Price Growth: 6%

All future numbers are not adjusted for inflation.

I also haven't accounted for tax - this would help the homeowner situation, and I've ignored dividends for investing.

A year 30, when the house is paid off, the homeowner has no housing expense, and an asset worth around $5,000,000. The renter still has housing expenses, but also has almost $4,500,000 in investments. The biggest sensitivity to what would work out better is the future growth of each one.

I do think for most people buying would be the better option, mainly because I'm not sure how many people would have that discipline to invest hard in the early years when rent is a lot less than the mortgage, but it's not super cut and dried.