息 stacks 自 — originally a picture of a nose — over 心, the heart. Breath traveling from nose to heart: to breathe, and by extension to catch one's breath, to rest.
息 is the pause in China's busy grammar: 休息 (to rest — the word your teacher says before break). 消息 is news — 'breaths' of information passing between people. 利息 is bank interest — money's quiet breathing while it sits. From nostrils to newsfeeds to compound interest, 息 is whatever flows gently in and out.
Nose 自 over heart 心 — breath settling: REST.
自 meant 'nose' first — Chinese people still point at their nose to say 'me'. 息 keeps the old nose breathing.