Do I buy my parents home?

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My Parents divorced with a house worth approximately 600k. There's a 200k mortgage left. My mom wants $150kish to buy out her half of the house. Me and my father currently live in the house. He has enough $ for the rest of the 10 year mortgage + bills (Social Security, Retirments accts)

Would it be financially wise to buy out my mom in this situation or should I just let them sell my childhood home? Currently Zillow estimates 5% appreciation yearly of the house in the current neighborhood/city it's in.

I would own half the house for roughly 150-180kish and my dad would continue to pay off all the bills/mortgages. He has also reiterated that I would get the entire house later in life, contracts signed etc.

I'm in a strut and would love some help. I am liquid enough to pay her off but would be most of my savings. I'm young 20s so I'm not sure if that makes a difference or not in this situation. I really wanted to get into real estate investing soon so I am kinda scared to try and refinance and stuff and work out a mortgage with my name because I wanted to FHA a multifamily in a few years so I feel like giving her cash is my only option..