ON THE VALUE OF REVERSIONS. 219 



which would be paid if the same party made the same 

 insurance at the present time. Find the present value 

 of an annuity on the life of the party insured, of the 

 same yearly amount as the preceding difference,, and this 

 value, increased by one year's purchase, is the present 

 value of the policy. 



To find the value of the policy immediately after 

 a premium is paid, add the premium just paid to the 

 result of the preceding rule. It would not be worth 

 while, in the present work, to give a rule for any in- 

 termediate value. (See Milne, p. 283.) 



Bat in finding the real value of a policy, there are 

 one or two circumstances to be considered, of which no 

 mention is made in the preceding rule. The buyer of 

 the policy, being uncommitted by any previous act of 

 his own, is not bound to consider the premium of any 

 one office as a standard. Suppose that in the preceding 

 example, another office of equal solvency can be found, 

 which will insure a life of 50 at 4 per cent, instead 

 of 5 : the buyer, therefore, may consider that the 

 seller offers him for 31. a year during his life a benefit 

 which he might buy elsewhere for 4/., and that he 

 should therefore pay only the value of an annuity due 

 of IL instead of 2. But since the two offices cannot 

 be together parties to any transfer of policy, the pre- 

 ceding case will only serve to show that it may be 

 more prudent for a person who has money to invest, to 

 lay it out at once in insuring lives in a cheap office, 

 than in buying existing policies in a dear one. It is to 

 be remembered that the lower premium in the preceding 

 rule is to be paid, by bargain already existing, while 

 the higher one is hypothetical, depending on the 

 buyer's opinion of tables of mortality. That the office 

 which demanded and obtained the SL would demand 

 the 51. for an insurance now to commence, must be no 

 consideration for a person who is merely thinking how 

 to lay out his money to the best advantage ; it may be 

 by buying the policy which is offered to him, or by 

 insuring his own life, or that of some one else, in the 



