Is ageing an inherited or acquired trait?

Ageing, senescence and death have no direct survival benefit for the individual or his/her genes. Does this trait survive because it manifests itself after the reproductive years are over? Ageing does not interfere with reproduction: so this allows this trait to survive. One can argue that the trait "cell death" has societal benefit, but this cannot explain it's persistence unless one uses teleological notions. Do all traits that manifest themselves after the reproductive years are over, tend to persist? Do elephants and tortoises have altered DNA's that promote longevity?