The Latin Programme offers a concise and thorough summary in answer to this question – well beyond simply improving SAT scores. Also a great apologetic for why Latin and Greek roots alone are insufficient. This was especially compelling:
Students with dyslexia often struggle to divide words into phonetic bits and then re-assemble these bits into a logical whole. Learning Latin allows them to understand the meaning of these pieces and this opens the door to a more in-depth comprehension of words. Dyslexics, even more than the general population, benefit from this aspect of Latin learning.
Read the rest at The Latin Programme.