The following problem, which has actually occurred in practice, presents several points of interest. It is hoped, therefore, that it may be found worthy of the attention of the Members of the Institute :–

A Survivorship Annuity of £100, payable half-yearly, till death, on (26) after (32), is to be paid for by an annual premium, returnable if (26) die before (32). Required the annual premium, which shall give to the grantor a profit of 15 per cent. ; the rates of mortality and interest assumed as those which will actually obtain, being Carlisle, 4%

The benefitto be paid for consists of two parts—first, the annuity, and secondly, the return of premium. The values of these are to be found separately.