Your entire billing history is available in Nutshell Setup. Any administrator can view payment amounts and dates. Your invoices are available to download as PDF files.

Click your avatar in the lower left corner of Nutshell, then choose Nutshell billing, on the far right of the page you'll be able to view and download your invoices.

You are automatically invoiced and billed on your monthly or annual billing date. You will also be invoiced if you upgrade your number of users.