Self-Service Payments for Contribution (Tuition)
You can certainly achieve this

Create a Contribution Page by enabling Other amount and payment processor.
Navigate to Administer &gt;&gt; CiviContribute &gt;&gt; CiviContribute Component Settings and select contribution page create at #1 for Default invoice payment page
Create a contribution for a contact with pending status.
On User Dashboard of contact (/civicrm/user?cid=[contact_id]) under contribution section you will see pay now button against the pending contribution. When clicked on pay now it will redirect to online contribution page where one can pay pending contribution online using credit card.

You can also generate the link to pay pending contribution online http://domainname.com/civicrm/contribute/transact?reset=1&amp;id=[contribution_page_id]&amp;ccid=[contribution_id]

where contribution_page_id(id) is contribution page id created at #1 and contribution_id(ccid) is contribution id created at #3.