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Scenarios for a 25 yo finishing a PhD staying in Academia, but hope to invest her $100 K USD

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1 1 Suppose 1: I am a 25 year old just about to finishing my PhD in pure mathematics, and have saved about $100 K USD so far in my life. I have saved all $100 K USD in an American Bank (actually Bank of America). Actually all $100 K USD can be used for investment, because I have additional saving (like extra $50K USD for backup). Suppose 2: You are senior and more intelligent in finance and investment issue. You wanted to give me some serious advices. What would you recommend me to do with this $100 K USD in the upcoming years? Say the next 10 or 20 years, and I am staying in USA. i.e., Best secnario for a 25 yo finshing a PhD, focus a career in Academia but invest her $100 K USD at hand Suppose 3: I would still focus most of my time doing research as I am applying my postdoc in pure mathematics...