; (ii) based on such claim, and after the veteran attained such age, the Secretary first determines that the veteran has a service-connected disability; and (iii) the veteran submits the application for such insurance during the two-year period following the date of such determination. (4) (A) A veteran enrolled in the insurance program under paragraph (1) may elect to be insured in any of the following amounts: (i) $10,000. (ii) $20,000. (iii) $30,000. (iv) $40,000. (v) In accordance with subparagraph (B), a maximum amount greater than $40,000. (B) The Secretary may establish a maximum amount to be insured under paragraph (1) that is greater than $40,000 if the Secretary— (i) determines that such maximum amount and the premiums for such amount— (I) are administratively and actuarially sound for the insurance program under paragraph (1); and (II) will not result in such program operating at a loss