I dont like it. You have the name of the person who sent you the letter, so that is what you use in the reply. I wouldn't address them as "Dear Wrights", maybe "Wright Household". I am not keen on your opening sentence either. "I hereby" sounds a bit too formal.
Dear Mr Wright,
In regard to your letter. I deeply regret any distress that the noise may have caused you, or your family, and I undertake not to repeat this in future.
Thats your apology done. Since we have to explain the reason, we can do that next.
A lot of information there, hey buddy, I dont care about your life. I certainly dont care about your homework or how it complicates your life. So keep it sweet and simple.As you must be aware this is a firt from my side and the readon for it is a genuine one. I have been assigned the task of watching documentary films for the final report of my part-time MA class. Since i work fulltime in the day time, i have no other choice but to finifsh the assignment in the evenings and late night. For some reason i didnt realise the noise would be causing disturbance to all in neighborhood.
The noise was due to my watching documentaries as part of my college course. I didn't realize it could be heard outside my apartment.
You solution is reasonable enough.
I shall prevent a recurrence by using headphones from now on
Student or Learner