I don't know what a life insurance annuity is.  Just an annuity that, like most of them, is sold by a company that also sells life insurance?  Or an annuity that also has a life insurance "kicker" that pays more than its cash value if the owner dies, so the "loss" is more than likely due to the life-insurance premium included in the price?  Those used to be popular.  Haven't seen any lately.  Agents make more money selling annuities with a long-term-care "kicker."