Abstract
It is sometimes overlooked that any Makeham joint-life annuity value at any arbitrary interest rate may be calculated to any required degree of accuracy by using the first few terms of one of two alternative series expansions. Moreover, tables (Pagurova, 1961) are now available that eliminate the need for this series evaluation in a great number of cases. This observation is of much wider application than may appear at first sight. It is well known that almost any 30-year range of ages in an arbitrary mortality table can be successfully regraduated using a Makeham formula. Since a life annuity deferred for 30
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