We begin by examining the accumulated value functions of some annuities-certain. We then investigate the accumulated value of these annuities where the interest is a random variable under some restrictions. Calculations are derived for the expected value and the variance of these accumulated values and present values. In particular we will examine an annuity-due of k yearly payments of 1. Then we will consider an increasing annuity-due of k yearly payments of 1, 2, ⋯ , k. And finally, we examine a decreasing annuity-due of k yearly payments of n, n - 1, ⋯ , n - k + 1, for k ≤ n.
Finally we extend our analysis to include a contingent annuity. That is an annuity in which each payment is contingent on the continuance of a given status. Specifically, we examine a life annuity under which each payment is contingent on the survival of one or more specified persons. We extend our methods from the previous sections to derive the formula of the expected value for the present value of the life annuities of a future life time at a random rate of interest.
","abstract_html":"<p>We begin by examining the accumulated value functions of some annuities-certain. We then investigate the accumulated value of these annuities where the interest is a random variable under some restrictions. Calculations are derived for the expected value and the variance of these accumulated values and present values. In particular we will examine an annuity-due of <em>k</em> yearly payments of 1. Then we will consider an increasing annuity-due of <em>k</em> yearly payments of 1, 2, ⋯ , <em>k</em>. And finally, we examine a decreasing annuity-due of <em>k</em> yearly payments of <em>n</em>, <em>n</em> - 1, ⋯ , <em>n</em> - <em>k</em> + 1, for <em>k</em> ≤ <em>n</em>.</p> <p>Finally we extend our analysis to include a contingent annuity. That is an annuity in which each payment is contingent on the continuance of a given status. Specifically, we examine a life annuity under which each payment is contingent on the survival of one or more specified persons. We extend our methods from the previous sections to derive the formula of the expected value for the present value of the life annuities of a future life time at a random rate of interest.</p>","abstract_has_math":false,"creators":["Baker, Lesley J."],"institution":null,"degree_name":"MS (Master of Science)","degree_level":"Thesis - unrestricted","degree_discipline":"Mathematical Sciences","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2001,"date_issued":"2001-08-01T07:00:00Z","date_published":"2001-08-01T07:00:00Z","updated_at":"2026-07-24T02:19:07Z","subjects":["Life Annuities","Random Interest Rates","Annuities","Physical Sciences and Mathematics"],"languages":[],"rights":["Copyright by the authors."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://dc.etsu.edu/etd/135","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Baker, Lesley J."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["1900-01-01T08:00:00Z"]},{"key":"dc:date.issued","label":"Date","values":["2001-08-01T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematical Sciences"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis - unrestricted"]},{"key":"thesis:degree_name","label":"Degree Name","values":["MS (Master of Science)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Life Annuities","Random Interest Rates","Annuities","Physical Sciences and Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["Copyright by the authors."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://dc.etsu.edu/context/etd/article/1185/viewcontent/bakerl0809.pdf","https://dc.etsu.edu/etd/135"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We begin by examining the accumulated value functions of some annuities-certain. We then investigate the accumulated value of these annuities where the interest is a random variable under some restrictions. Calculations are derived for the expected value and the variance of these accumulated values and present values. In particular we will examine an annuity-due of k yearly payments of 1. Then we will consider an increasing annuity-due of k yearly payments of 1, 2, ⋯ , k. And finally, we examine a decreasing annuity-due of k yearly payments of n, n - 1, ⋯ , n - k + 1, for k ≤ n.
Finally we extend our analysis to include a contingent annuity. That is an annuity in which each payment is contingent on the continuance of a given status. Specifically, we examine a life annuity under which each payment is contingent on the survival of one or more specified persons. We extend our methods from the previous sections to derive the formula of the expected value for the present value of the life annuities of a future life time at a random rate of interest.
"]},{"key":"dc:title","label":"Title","values":["Life Annuities under Random Rates of Interest."]}]}],"canonical_facts":{"dc:creator":["Baker, Lesley J."],"dc:date.available":["1900-01-01T08:00:00Z"],"dc:date.issued":["2001-08-01T07:00:00Z"],"dc:description.abstract":["We begin by examining the accumulated value functions of some annuities-certain. We then investigate the accumulated value of these annuities where the interest is a random variable under some restrictions. Calculations are derived for the expected value and the variance of these accumulated values and present values. In particular we will examine an annuity-due of k yearly payments of 1. Then we will consider an increasing annuity-due of k yearly payments of 1, 2, ⋯ , k. And finally, we examine a decreasing annuity-due of k yearly payments of n, n - 1, ⋯ , n - k + 1, for k ≤ n.
Finally we extend our analysis to include a contingent annuity. That is an annuity in which each payment is contingent on the continuance of a given status. Specifically, we examine a life annuity under which each payment is contingent on the survival of one or more specified persons. We extend our methods from the previous sections to derive the formula of the expected value for the present value of the life annuities of a future life time at a random rate of interest.
"],"dc:identifier":["https://dc.etsu.edu/context/etd/article/1185/viewcontent/bakerl0809.pdf","https://dc.etsu.edu/etd/135"],"dc:rights":["Copyright by the authors."],"dc:subject":["Life Annuities","Random Interest Rates","Annuities","Physical Sciences and Mathematics"],"dc:title":["Life Annuities under Random Rates of Interest."],"thesis:degree_discipline":["Mathematical Sciences"],"thesis:degree_level":["Thesis - unrestricted"],"thesis:degree_name":["MS (Master of Science)"]},"updated_at":"2026-07-24T02:19:07Z"}