Should an 85 year old woman buy an annuity?

That all depends on the purpose of the annuity. If it is money that will be transferred to an heir and is not needed to live on or to have as an adequate amount of liquid assets then there is nothing wrong with this. But other factors to consider are anticipated added expenses, a decrease in future income, or if the purchase of this product reduces the needed amount of liquid assets. If the responses to these factors are no and the sole purpose is to pass the money on as an estate, then there is nothing wrong with this purchase so long as the individual is of sound mind and understands the product she is purchasing.