Dear [Recipient's Name],
I am writing to sincerely apologize for [clearly state the reason for the apology, e.g., my mistake yesterday, the inconvenience caused, the delay in delivery, etc.].
I understand that my actions/inaction resulted in [specify the consequences, e.g., disrupting your plans, causing you frustration, creating extra work for you]. This was entirely my fault, and I take full responsibility. I want you to know that there is no excuse for what happened.
To make things right, I have [describe the corrective action you are taking, e.g., already fixed the issue, will ensure it never happens again, would like to offer to compensate you in the following way…]. I am committed to ensuring this situation is resolved.
Once again, I am truly very sorry for the trouble and disappointment I have caused. I value [our relationship/your business/your trust] highly, and I hope you can accept my heartfelt apology.
Sincerely,
[Your Name]
[Date]