Dear {Recipient},
On {date}, I accidentally damaged your {broken object}. While the damage was entirely accidental, I do take full responsibility and I am deeply sorry. I have already offered to pay {item's worth}, which you listed as the item's value, and made arrangements for repairs myself. However, I do not think this fully conveys how sorry I am to have inconvenienced you.
So, again, thank you for your patient attitude concerning your {broken object}. I am not sure I myself would be so cool headed were our positions reversed.
In happier news, you can expect the fully repaired {broken object} on {date of repair}.
Thanks again, and I will be seeing you soon.
Sincerely,
{Sender}
