Office Premiums   81

pay the premium for age 30 and agreeing that only one half of the sum assured shall be payable in the event of death during the first n years.

To find n, we have

1   1
Pao • a 45 —A45 - -IA 45 ~tl .

If we have a table of Ax;,l we can enter it inversely opposite x=45 with the value 2[A45—P30 . a45] to find n. Or, using commutation values, we have

N30 N45 _ M45 +M45+n lr 30 D45   2D45

M45+n = 2   H30 X N45 — 145 N30

from which n can be found.

Where offices are protected by agreements among themselves against rate-cutting almost any method which is agreed upon may be used in calculating the office premiums so long as the resulting premiums are abundantly safe. But where competition is allowed free play office premiums should be calculated from select rather than from aggregate or ultimate tables, and the rate of interest used may be close to the rate which the office expects to earn.

therefore

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