Mr. Spens on Life Inmrance. 221 



tween the values stated opposite 45, in columns 2 and 3 ; and 55, in 

 the same way, between the values in columns 3 and 4. It is also neces- 

 sary that the difference between the values at one age, and the next 

 age,'should be less than in the general table : this may be readily per- 

 ceived must be the case, as where the annuities increase from the point 

 of agreement towards the younger ages, less sums must be added to the 

 separate class values, to make them lower than the others ; and where 

 they decrease towards the advanced ages, less sums must be subtracted 

 to make the values in the separate classes greater. 



Table II. has been made out, having all these points in view, but 

 it was found impossible to make it harmonise entirely with them all. 

 The chief difference appears to be in my being obliged to state the 

 values from 39 to 45, almost in accordance with the values stated 

 above, in column H 2. They ought of course, looking only to that, to 

 be stated higher ; but had this been done, 45 in H 2, would have been 

 made about equal to 45 in H 3 ; and the regulation of the lessening 

 of the differences would have been interfered with. It may be that 

 the values alluded to in H 2, are accidentally higher ; but the num- 

 bers of observations on lives and deaths from which they are deduced, 

 are rather considerable, and perhaps the observations are correct, in 

 leading us to the conclusion that lives selected about these ages are 

 little better than lives selected a few years earlier which have arrived 

 at these ages. It will be observed that Table II. has been extended 

 back to age 20, which I thought could be very safely done by observa- 

 tion of the differences at the higher ages, and in Table I. 



8. From Table II, Table III. is deduced of the minimum annual 

 Premiums for Life Insurance, on the assumption that by means of in- 

 terest and profit, less expenses, money is accumulated at 4 per cent. 



9. In regard to the annual values of annual or periodical additions, I 

 shall restrict myself to the values according to the systems stated below 

 at ages 20, 30, 40, 50, and 60, and for reasons to be afterwards no- 

 ticed, shall make the calculations according to the Carlisle Tables. 

 The rate of interest assumed is as before, four per cent 



1st. Annual values of simple additions of One Pound, made every 

 year, that is. One Pound if the party survive one year, and another 

 Pound if he survive another year, and so on. 



2d. Annual values of additions of 1 per cent according to the sys- 

 tem of the London Equitable, declared, say every seven years ; that is 

 supposing additions at the rate of 1 per cent., 7 per cent at the end of 

 seven years, other 14 per cent, at the end of the next seven years, at 

 the end of the next seven, 21 per cent more, and so on. 



