As an administrative professional in the finance department, you are responsible for generating and managing invoices for a company. In this scenario, you encounter a math problem related to calculating invoice amounts, applying discounts, and determining the due date. 

Problem Description: 

You need to communicate an invoice to a client based on the services provided. The total invoice amount is $10,000. The payment terms for this client specify that if the invoice is paid within 10 days, a 5% discount can be applied. After 10 days, the full invoice amount is due. The invoice date is September 1, 2023. It is your job to communicate the due date, discount terms, and the total amount payable clearly to the client. 

Write out a professional email to the client and provide the necessary information on the invoice, including the due date, discount details (how much is due if it is paid within 10 days? 

How much if it's paid after 10 days?, and payment instructions.