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How to calculate pro-rata investment size for a follow-on investment?

Say a VC has invested $3M in last round which had a post-money valuation of $15M, and that investment gave her a 20% stake in the company. And she was given the pro-rata rights for future round(s).

The current round now has a post-money valuation of $30M, in order to pro rata her investment, does it mean that the VC needs to put in another 30*0.2-3 = 3M to maintain her 20% stake after this round?

Is that how it works?

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