Beginning of an apology letter

[ziawj2]

I lost a book borrowed from my friend. When I write an apology letter, I feel confused in the ways:
1. In an apology letter, which is more common begin with, a statement of regret, a statement of appreciation or a question? For example, I lost a book borrowed from my friend. If I wrote:
1) I’m sorry I lost your book borrowed two months ago.
2) Do you remember the book I borrowed from you two months ago. I’m sorry to tell you that I lost it.
3) Thank you for lending me your book. But unfortunately, I lost it.
Of these three beginnings, which is more common in your opinion? Thank you.
To be concise, I think “to tell you” is a little wordy because I’m writing to “you” , I’m talking with you, so there is no need to write “to tell you”. What is your opinion?

2. In the middle of the letter, I think the sentence "I know you understand me" is a little direct. Will it better if I change it to "I hope you will understand me".

3. Maybe there are problems in the terms of grammar, but when I read it, it sounds unnatural. Could you help me check in terms of language style? Thank you.

I’m really sorry for losing your book which you lent to me 2 months ago. I have ready to return it to you tomorrow. Unluckily, I realized that I lost it by mistake during my moving to this new apartment a week ago. I know this book means a lot for you. Please give me a chance to make up to you. How about buy a new one for you ? I just have been told that there is a special bookshop which I can find this book. I promise to get the book and give it back to you as soon as possible. I hope this won’t upset you that much. I hope you’re not too mad at me.

[Tdol]

The second works best for me as it tells the person what you're talking about and what happened. Also, with letters to friends, it's more about communicating with someone you know than following a formula. What do you think would work best in this situation? Talk to your friend and say what you want to say- friends will understand. As long as it's not a priceless first edition, it can be sorted out.

[ziawj2]

I prefer the second because it directly tells me why you wrote, and I, of couse, remembered I have lent you a book.
Could you tell me your opinions about question 2 and 3. Thank you very much.