expression, godan verb (-ru, irregular)
be effective; be worthwhile; pay off
Expresses that an action or effort yields a worthwhile result, reward, or effect. Often used in the pattern 〜した甲斐がある (the effort of doing ~ was worth it).
一生懸命勉強した甲斐があって、試験に合格した。
All that hard studying paid off—I passed the exam.
This book was worth reading.
From the noun 甲斐 (かい, 'effect, worth') + がある ('there is'). The noun 甲斐 itself is of uncertain origin, possibly related to 替える (かえる, 'to exchange') or 交わす (かわす, 'to exchange'), suggesting a return on effort.