First, remember that the first letter of a sentence and proper nouns (like Sunday) start with a capital letter.
Second, the TONE is what is informal. "Just to let you know" is very casual. "I am writing to let you know" is more formal. "I am writing to inform you" is quite formal. Do you have the right to "inform" the person reading this that you will be late, or do you need to request permission to be late? (Are you the boss or are you the employee?)
Phrases like "show up" are also casual. I don't "show up" at work - that sounds like I'm not there to work; I'm simply present. It's a very casual approach to your job.
I need to attend to some business at the bank, and I would like to do so on Sunday morning. I don't know how long it will take, but as soon as it is completed, I will come directly to work. Please let me know if my late arrival will present any difficulties, and if so, I will make other arrangements.
- For Teachers