اكمل/اكتمل both of them from كمل =complete ..but اكمل is doing in purpose with effort from us (اكملت واجبي=i completed my home work)...اكتمل=we dont have some thing to do with it (اكتمل القمر=moon is completed become <full moon> and of course we cant control in it ..generally this ت sometimes add to verb to show there is something more than we used to ..notes this Aya ..فَمَا اسْطَاعُوا أَنْ يَظْهَرُوهُ وَمَا اسْتَطَاعُوا لَهُ نَقْبًا ) الكهف97 you can follow that link to know more about https://islamqa.info/ar/answers/246191