Any Korean resident or non-resident who carries in less than USD10,000 into Korea doesn't need to declare it with the customs.
If the amount exceeds USD10,000, you are required to declare it when entering Korea. But no customs duties, taxes or fees will be imposed.
Customs officials may request to see the entire money for verification.
Let's say you brought in $18,000 USD, declared it, but you only spend $4,000 in Korea. If you carry out USD14,000 after bringing in USD18,000, you don't have to get approval from or declare with the Bank of Korea. (under the Foreign Exchange Transactions Regulation Article 6-2)
What happens if I am bringing in more than $10,000 USD and I don't declare it to just skip the paperwork and fuss.
You may be subject to less than 1 year of imprisonment or less than 100 million won of fine under the provisions of Article 28 of the Foreign Exchange Transactions Act of Korea.
Source: Korea Customs