Surely your friend knows whether you are a sincere person, so she will know whether you really plan to buy her a replacement book.
Originally Posted by ziawj2
With your second example, do you hope that your friend doesn't mind that you lost the book or that you will do anything to compensate her for the loss. If she is a good friend, your second sentence is rather formal.
I would write something like "I'm really sorry. I've lost that book I borrowed from you. I know it was valuable but I'll buy a new one and get it to you as soon as possible. I hope that's OK."
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.