How much do I need to start investing in robos? I know there's no minimum amount for some, but what would be the minimum amount to avoid excessive fees?

You can start at $1. There is no real excessive fees problem - as compared to traditional brokers. The fees are scalable, you can start wondering about them once your nest egg reaches $30,000.

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Different robo-advisors charge different fees but it ranges from 0.2% - 0.8% if I’m not wrong.

Depending on which robo-advisor you’re interested in, some have minimum amount & fees for every withdrawal etc