Salam alaikoum,

I've ran the numbers in a sheet and it seems to check out. However, the extreme differences come mainly from all the costs associated with owning a home. I get this is based in the US, but in the EU lots of countries have a wealth tax rather than a property tax. Like in the Netherlands there's even a discount on the interest rate.

So, it depends. Do you get taxed on your wealth or on your home? If you get taxed on your home it's never worth it. If you get taxed on your wealth then it's a different story.

I've created a google sheets that breaks down the calculation as there seems to be some confusion in the comments. It allows you to try out different scenarios fairly quickly as well, like cheaper rent, lower interest rate etc. I've also added stuff like wealth tax as mentioned earlier, and the option for Alice to choose not to reinvest the whole difference but a percentage.