Let us consider an example where you create an invoice on 20th July. You mention in the Customer Notes section that if the customer pays before 25th July, he/she gets a discount of 10% on the invoice amount i.e. if the invoice amount is $100, the customer gets a discount of $10 and he/she will need to pay only $90.
Once the payment of $90 has been made, the status of the invoice will change to Partially Paid after which you must edit the invoice and enter the value -10 either in Adjustments or Discounts and click Save.
In the pop-up that follows, enter the reason for editing an invoice that has already been sent and click Save.
Finally, the status of the invoice will be changed to Paid.