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I've found a phrase "an additional $30,000 in income" in a government document. Is the article an correct there and why?

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Yes it is.

If there is an adjective or an adverb-adjective combination before the noun, A(AN) should agree with the first sound in the adjective or the adverb-adjective combination.

Examples:

  • He is an excellent teacher.

  • I saw a really beautiful eagle at the zoo.

Source.