Difference between to know and to understand in Korean
알다·납득하다

알다to know
알다 (to know) means to have information in your mind or to be familiar with someone, something, or a place. You use it when you know a fact, know a person, or know the answer. It is very common in daily Korean, especially in sentences like "I know" and "Do you know?".

납득하다to understand
납득하다 means to understand something and feel that it makes sense. You use it when you hear a reason or explanation and accept it. It is common for rules, decisions, prices, and other situations where you say, “Okay, I understand now.”
The difference
알다 means to know a fact or be aware of something. It does not mean you were persuaded by a reason or explanation.