Final answer:
The designation by the federal government for an individual's eligibility to receive a Veterans Administration loan is known as a VA loan, which is a mortgage loan program guaranteed by the U.S. Department of Veterans Affairs for American veterans and select family members.
Step-by-step explanation:
The correct answer to the question "A designation by the federal government of an individual's eligibility to obtain a federal Veterans Administration loan" is A. VA loan. A VA loan is a mortgage loan in the United States guaranteed by the United States Department of Veterans Affairs (VA). The program is for American veterans, military members currently serving in the U.S. military, reservists and select surviving spouses (provided they do not remarry) and is designed to offer long-term financing to eligible American veterans or their surviving spouses. The VA loan is intended to supply home financing to eligible veterans and to help veterans purchase properties with no down payment.