Partly paid shares

This has got to be a private company with only $100 shares

To the best of my knowledge, there’s no minimum payment necessary. In fact, I remember having an investment in a company that reduced its share capital (another of my great investments!) where my holding of, say, 400 shares of £1 each fully paid became a holding of 400 shares of 10 pence each credited as 1 pence paid. And then the company called up the remaining 9 pence per share

Back to your question, where the company wishes to issue 100 partly paid shares at a premium of $1 per share, I suggest the minimum amount payable would be $1.01 per share

Does that answer you?