"My internship will end at the end of August" is the most natural to me. "My internship will end by the end of August" doesn't sound right but could work "My internship will end until the end of August" is completely wrong - The correct sentence when using until, should be "My internship will last until the end of August" My internship will end is correct. If you want to use "will be", you have to say "My internship will be ending (at the end of August") I hope this helps.