済 means “finish, settle”

すむ · sumu

Also: settle (debt, etc.), relieve (burden), come to an end

Kun'yomi (Japanese reading)
すむ, すまない, すます, すくう, なす
On'yomi (Chinese reading)
サイ, セイ

JLPT N3 · Taught in grade 6 · 11 strokes

The story

Water (氵) beside 斉 (even): picture a river crossed and an account settled. 済む means "to be done", and すみません literally says "it isn't settled": an apology that admits a debt not yet repaid.

Used in 済む (sumu, to be finished), 経済 (keizai, economy), and 返済 (hensai, repayment)

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Readings from KANJIDIC2, © EDRDG, CC BY-SA.