The official joining-family description covers a spouse and unmarried children under 21, not a parent as your dependent. Do not assume payment creates eligibility. Adding a qualifying relative to your application is a step within your case; establishing a route for someone the published terms do not identify is a separate case with a separate applicant. The published description names a spouse and unmarried children under 21 as joining family. A parent of an adult applicant falls outside that description, and no amount paid changes which description applies.
Identify the parent’s actual route
A separate possible application requires its own review. Financial dependence, a shared household or the parent’s contribution to your gift does not itself place the parent in the published derivative group. Ask what the parent would be applying for, in their own name, before asking what it costs.
The published individual route requires the parent’s own eligibility and admissibility to be established, and the payment sits at the end of that assessment rather than at the start of it. Other immigration options may or may not exist for a parent; this page does not decide it. What can be said plainly is the structure: the money is paid by the applicant to the U.S.
government under the published terms, it is not a benefit conferred on the applicant by the government, and it does not create a relationship category that the terms do not contain.