222 Me. Spens on Life Insurance. 



Ages 20 30 40 50 60 



Values 1-013 1-028 -998 -908 -756 



In this mode of division the values are much affected by the intervals 

 at which the allocations are made ; thus, supposing them to be made 

 quinqueuniallj, at age 40, the annual value will be 1-408; if sexen- 

 eniallj, 1-169 ; and if decennially, -691. 



In the above two cases, greater or less rates of additions will be 

 simple proportions of the above. 



3d. Annual values of additions accumulated, say septennially, and 

 with a provision that no addition shall be paid if the party die within 

 five years. In this case, the different rates of addition are not simple 

 proportions of one another, and I have therefore stated the values of 

 additions at the rates of 1, li and 2 per cent. 



AGES. VALUES OF ADDITIONS. 



1 ^ cent. Ji ^ cent. 2 ^ cent. 



10. I have stated the above annual values of additions, according 

 to the Carlisle Tables, partly because for the most part I had some 

 time ago calculated them according to these tables, and further, be- 

 cause I am satisfied that the values thus brought out must be very 

 nearly the true ones. Indeed it will be seen from the small difference 

 between the values at the ages ten years different, that any such cor- 

 rection on the rate of mortality as might be made, could to a very 

 small extent affect the results. 



1 1. Assuming that we have now made a near approximation to the 

 true premium, and the true values of annual additions, these afford 

 the best means for testing the fairness of modes of allocations of bonus 

 additions. 



12. Under one system of assurance, a definite premium is fixed for 

 a definite guaranteed sum, the rate of premium being stated at such 

 sum as may be expected to yield a profit to the assurers in lieu of 

 their guarantee. Under the other system, parties associate together 

 to assure one another, and it has been generally thought desirable to 

 provide against any extraordinary mortality, or unprofitableness of 

 money, and to give the utmost confidence in such Society, that the 

 rates should be, and should be considered by the public to be, such as 

 will undoubtedly yield a surplus. Such are the two general systems 

 on which assurance by proprietory offices and by mutual societies 



