Apologising by email - translated

How to apologise to a client via email ?
如何通过电子邮件向客户道歉?
client 英 [ˈklaɪənt] 美 [ˈklaɪənt]
n.客户;当事人;委托人;(连接在服务器上的)客户机
1. State the error
It has come to my attention that you were overcharged $623 on invoice 0415 due to a pricing error by our organisation.
2. Apology #1
I would like to sincerely apologise for this error, and we acknowledge the inconvenience this will have caused.
3. Explain the error
Unfortunately, there was a glitch in our invoicing system, and l can see that item 02 did not have the correct discount applied, which explains the $623 overcharge discrepancy.
4. How you will resolve the error
We appreciate that prompt payment of the invoice was made on the 1st of March, and have therefore applied a credit of $623 to your account.
I have also added a further $100 credit to the account as a gesture of goodwill.
- This is a really good phrase to remember if you want to do something for someone free of charge --- a gesture of goodwill
5. Give reassurance
reassurance 英 [ˌriːəˈʃʊərəns; ˌriːəˈʃɔːrəns] 美 [ˌriːəˈʃʊrəns]
n. 安慰,慰藉;能消除疑虑的说话(或行动),保证
As your account manager, l should have checked the invoice more closely before issuing it.
Please be assured that l will check invoices more closely in the future.
6. Apology #2
Again, I am very sorry for this error.
Kind Regards
Sophie