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I have some information about adding price rules to a customer's account. The Customer Type section is used to categorize your customers in ways meaningful to your business (Example: Retailer or Wholesale). That said, utilizing this portion to add a new price level isn't possible.
You'll want to enter the discount manually on the invoice or on the received payment page as a workaround. Here's how:
To manually add the discount in the invoice, just override the Amount column.
From the Receive Payments page:
Additionally, here's a link that covers all the tasks you can do when using the customer feature: Topics about your company's income and customers.
Have concerns or follow-up questions about price levels? Drop them anytime and I'll be happy to answer them for you. Take care and have a great rest of the week.