期日
きじつ · kijitsu · JLPT N1 · noun
date
期 — 其 (phonetic) + 月 (moon/time)
期 is a phono-semantic compound. The right side 月 (moon) signals meaning, since lunar cycles marked fixed time periods in ancient China. The left side 其 supplies the sound. Together it points to a set time, period, or appointed date — meanings still carried today in words like 期间 and 日期.
日 — pictograph of the sun
日 is a pictograph of the sun, originally drawn as a circle with a dot or stroke inside representing the sun's substance. Over time the round shape was squared off into the modern rectangular form. It means 'sun' and by extension 'day'.