Role/Capability required to upgrade website or renew payment

I am attempting to created a limited user that has the ability to upgrade or make a payment so they need access to the "your account" features.

What particular (minimum) role/capability do I need to assign the user in order to accomplish this? I'm not looking for an answer like "administrator", "contributor", etc... I need to know the capability(s) like "delete_posts", "manage_network_options" for example. Which one(s) are needed to provide this capability.