220 ESSAY ON PROBABILITIES. 



same or another office. It is his business to consider 

 what he is likely to have to pay, in the shape of future 

 premiums, and not what an office, which must he on 

 the safe side, has thought fit to suppose it will have to 

 receive. Putting out of view the state of health * of 

 the party insured, I should think it most advisable to 

 calculate the value of policies by finding the present 

 value of the sum insured, and also that of the premiums 

 to be paid, from the tables which best represent healthy 

 life, and using the rate of interest which money will 

 really obtain, rather above than below ; that is, I should 

 use the Carlisle tables at 4 per cent. The profits 

 guaranteed by the office, if any, should be duly con- 

 sidered. Thus suppose a person at the age of 30 had 

 insured for 10001. in an office which demands 25 /. 

 premium for that insurance, and returns no profits, 

 and suppose that twenty years have elapsed, so that the 

 life insured is now at the age of 50, what is the real 

 value of his policy? The value of II. to be received at 

 the death of a person aged fifty, by the Carlisle tables 

 at 4 per cent., is (p. 214.), 25 12'9 divided by 25 -4- 1 

 or '465 : that of WOOL is therefore 465/. If a premium 

 be just becoming due, the present value of all the 

 premiums is therefore 1 -f 12*9 or 13'9 years' purchase ; 

 and 13'9 X 25/. is 347'5/. Consequently 465- 347|, or 

 117^., is what I should consider to be the value of that 

 policy. But if I took the tables of the same office, 

 which require a premium of 47 /. at the age of fifty, 

 and which, with some variation, are derived from the 

 Northampton tables at 3 per cent., I should find by 

 the rule in p. 218., (1 + 12-4) x (47-25), or 295/. 

 nearly. So great is the difference between policies 

 valued by the nearest approximation which exists to the 

 actual truth, and then valued by the tables which 

 offices adopt for their own security. 



The office itself, which takes an advantage of the 

 buyer when the policy is first created, may reasonably 



* Of course the policy of a person whose health has very much declined 

 since he effected the insurance, is of higher value on that account : but 

 this cannot be made the subject of calculation. 



