I often see donation requests with amounts in multiples of $18. I would like to know the source for giving charity of the numeric value of the Hebrew word chai (18) and its multiples.
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When charity is given as a form of merit, as opposed to a general tithing obligation, it is seen as an intercessor before God. This is termed a kataigor. Angels also play this role, especially the angel Michael. To attest to this symbolically or perhaps to request that this angel intercede and serve as a kataigor on our behalf there is a custom to give charity with the numerical equivalent of Michael - 101. This custom is still prevalent among Sefardic Jews.
Since giving 101 of a particular currency may not be feasible other numeric equivalents which were connected to angels were found. 18 stems from a kabbalistic understanding of a story in Chagigah 15b: Rebbi Mayer found a pomegranate (רמון) he ate the inside and cast away the husk. The kabbalists understood this to be a veiled reference to the angel מטטרון [MaTat]. The idea being that the letters of the word רמון are the outter letters of the name מטטרון. When those are removed you are left with ט-ט, the inner substance which is what Rebbi Mayer "consumed". The gematria value of ט-ט is 18, hence the giving of charity in multiples of 18.