Sam deposits 100 in a fund paying interest at an annual effective rate of 2X % for the first 5 years, and X% for the next 10 years. Sam invests the interest earned at the end of each year in another fund crediting interest at 4% effective. At the end of 15 years, the accumulated value of Sam's original deposit and his invested interest is 200. Determine X.

Please solve this question with formulas and writing it out by hand.