Asking for an apology is reassuring the reader that the mistakes will not be repeated and also it is one way of showing the guilt of making the mistake. There is not a single person in this whole world that is perfect. The other reason why people write an apology letter is that they can express to the reader the exact reason of the apology. In this way the reader also comes to know what exactly must have happened on the day when something went wrong. Hence it is the best way to apologize for the guilt of your mistake.
William C. Lacey
18 Barnaby Road
Date: 6th September 2010.
Subject: Sorry letter to cousin.
I want to apologies for using your car without your permission. On the earlier day when you were not at home, I was very much in need of taking your car as I was getting late for my evening lectures. I tried to call you on your cell phone but I was getting your call out of reach. It was also raining very heavily. All lines of the network were very busy. Due to less vicinity on my way to classes, the car got a slight scratch on its bumper.
I apologize for the same and I promise you that I will never use your property without taking your permission, no matter how urgency comes to me. I also assure you that I will pay charges for all the repairing work required for the cars maintenance. I hope you will surely forgive me for my mistakes and I hope u will understand the situation I was facing on that day.