Write an invoice and payment terms from work done

My business: {{my_business}}
Customer: {{customer}}
Invoice number and date: {{invoice_number}}, {{invoice_date}}
Tax to show: {{tax_info}}
How the customer can pay: {{payment_methods}}

What was agreed (quote, contract or email: rates, payment terms, any late fee clause):
"""
{{agreed_terms}}
"""

Work done (what was delivered, dates, hours or quantities):
"""
{{work_done}}
"""

Task: Write an invoice for the work above, plus a short email to send it with. It goes to the customer's accounts payable team, who will approve it only if they can match it to what was ordered. The goal is an invoice they can approve on first reading, so clarity matters more than polish.

Requirements:
- Line items: a description that names the deliverable and dates in the words of the agreement (for example, "Website copy, 6 pages, delivered May 12, per quote Q-114" shows the form), then quantity, rate and amount. Show each line's calculation.
- Use only the rates in the agreement. If the work done goes beyond what was agreed, list it separately for me to decide on; do not bill it.
- Subtotal, tax and total with the sums written out. Calculate tax only with the rate I gave; if I wrote "none", show no tax line.
- Payment terms: the due date as an actual date, worked out from the invoice date and the agreed terms, plus how to pay and who to contact with questions. Include a late fee only if the agreement contains one, worded as it is there.
- Include the customer's purchase order number if they have one, because many accounts payable teams reject invoices without it.

Format:
1. The invoice laid out top to bottom as plain text, ready to copy into my invoicing tool or a document.
2. The cover email: a subject line with the invoice number, and up to 80 words.
3. Missing details: anything an invoice normally needs that I have not given, such as a PO number or the customer's billing address.

If anything is missing, write [ADD: what is needed] in the invoice instead of inventing it. Do not invent tax IDs, bank details or contract terms.

Invoice and tax requirements differ by country and state, so have an accountant confirm the tax lines and required details before you rely on this layout.