Corrected email (polished):

Dear Cathleen,

Our EUR account number is: 54 1020 1042 0000 8402 0436 0244

We would appreciate it if you could send us proof of payment when the transfer is complete. Please confirm that our calculations are correct and that the reimbursement will be €9,953.70 (or €9.953,70 using European number format).

Thank you.

Kind regards,
[Your Name]

Simple step-by-step explanation of the changes (for a 13-year-old):

  1. "Our account number in EUR:" → "Our EUR account number is:" — This is a clearer, more natural way to say it.
  2. "I will appreciate it" → "We would appreciate it if you could" — "Would appreciate" is more polite and "if you could" makes the request softer and more formal. Also changed "I" to "We" because many business emails come from a team.
  3. "a proof of payment" → "proof of payment" — "Proof of payment" is an uncountable noun phrase here, so we don’t need "a."
  4. "when ready" → "when the transfer is complete" — This is clearer: it tells Cathleen exactly when to send the proof.
  5. Spelling: "reimbirsement" → "reimbursement."
  6. Number format and punctuation: write the amount with a currency symbol and consistent punctuation. I used €9,953.70 (English style) and showed the European style €9.953,70 in parentheses so there’s no confusion.
  7. Added a polite closing: "Thank you." and "Kind regards," plus your name — standard for business emails.

If you want, tell me whether you prefer the English or European number format and I can put the amount in only that style. Also let me know your name and whether the email should come from one person or a team ("I" vs "we") and I will update the final version.