Can you build equity the same way through a private mortgage?

[Lauren Mattina]

I'm debating whether to purchase my mother's home through a private mortgage as a way to start house hacking but want to make sure I am able to build equity in a way that will allow me to use it to purchase a second property. My mom's house is paid off and she's willing to give me a great interest rate of about 2%. My husband and I would move into the main house and my mom will move into the basement apartment. She'll pay below market value for rent in NYC, but it will still help lower our monthly costs. We still have to get the house appraised and discuss purchase price, but wanted to know if this is something I should even entertain or just continue to save up for a down payment on a single family property in a more landlord friendly state without house hacking?

Thank you in advance for the replies.