It's a relative pronoun. It stands for 'whose $100'.
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Persian LearnerWhat's the form and function of the underlined part?It's an interrogative determiner, but the associated noun ($100) is omitted. Some grammarians call this a case of promoting the determiner to a pronoun. The complement of "wonder" is usually, as here, an indirect question. The corresponding direct question is "Whose $100 was it?"
Persian LearnerWhat is its function if we accept it as an interrogative pronoun?(possessive) determiner (It's possible that in the textbook you are using they call it a possessive adjective.)
Persian LearnerHow about if we answer the question this way?possessive pronoun
Persian Learnerwould you please check my analysis of the whole sentence?It looks really good. I think you've said everything that can be said about that sentence!