All three paths start with the same cash and the same monthly budget. Whoever needs the most upfront sets the bar; the other two invest the difference. Each month, whoever has the cheapest housing bill invests what they save — so every path puts out the same total each month, and the only question is where the money ends up.

The renter’s ending net worth is their investment account. The buyer’s and house hacker’s is their home equity (value minus selling costs minus the remaining loan) plus any side investments. For the house hacker, the tenant’s rent lowers the monthly housing bill, which means more goes into investments — and the duplex is usually a bigger asset building more equity. Whoever ends up with the most, wins.

Left out for simplicity: income tax in every direction (rental income is shown pre-tax, and mortgage-interest, property-tax and depreciation deductions are ignored), PMI, landlord headaches, and any lifestyle differences. This sizes up the money. It can’t tell you whether you want a tenant on the other side of the wall.