Why is the Korean word for "exchange rate" written as 환율 instead of 환률?

ANSWER: Because the 환 in 환율 (換率) ends in a ㄴ.

In Korea, the Chinese character 率 (률/율) can be written as either 률 or 율, depending on what word precedes it, and it can translate as "rate," "ratio," "proportion," or "percentage," also depending on what word precedes it. If the word that precedes 率 (률/율) ends in a vowel or the consonant ㄴ, then it is written as /율/, as in 비율 (比率), which can translate as "ratio," "rate" or "percentage," or as in 환율 (換率), which means "exchange rate." But if the word that precedes 率 (률/율) ends with any other consonant instead of ㄴ, then it is written as 률, as in 보험률 (保險率), which means "insurance rate"; 성장률 (成長率), which means "growth rate"; or 능률 (能率), which means "efficiency."

The above rules apply not only to the Chinese character 率 (률/율) but also to any Chinese character that can be written as either 률 or 율. So, for example, the Chinese character 律 (률/율), which can translate as "a law," "a regulation," or "commandments," is also written as either 률 or 율 depending on what word precedes it. 도덕률 (道德律), for example, can translate as "moral code," and 자연율 (自然律) can translate as "the natural law." 

The Chinese character 慄 (률/율) means "fear" and can also be written as either 률 or 율, depending on what word precedes it. For example, the Sino-Korean word for "to shudder or to tremble is fear" is 전율 (戰慄), which includes 慄 (률/율), the character for "fear." The reason 전율 is written as "전율" instead of "전률" is that its first syllable 전 ends in a ㄴ, so 전율 also follows the spelling rules mentioned above. By the way, besides meaning "war," the Chinese character 戰 (전) can also mean "to tremble," so the word 전율 (戰慄) can literally translate as "to tremble (戰) in fear (慄)" or "a trembling fear."