The expression that best completes the sentence “By the end of this year, … in this town for eleven years” is I’ll have lived.

This phrase indicates that by the end of this year, the speaker will have completed eleven years of living in this town.

Here’s why the other options are not correct:

• I’m living: This phrase is in the present continuous tense, which doesn’t fit well in this context because the sentence is referring to a future event.
• I’d be living: This phrase is in the conditional tense, which doesn’t fit well in this context because the sentence is referring to a future event that is certain to happen.
• I’ll live: This phrase is in the simple future tense, which doesn’t fit well in this context because the sentence is referring to a future event that will have been completed by a certain time.
• I have lived: This phrase is in the present perfect tense, which doesn’t fit well in this context because the sentence is referring to a future event.