326 3Ir. Lubbock on the Comparison of 



I have obtained, those which liave been obtained by other 

 writers. The same series, p. 324, line 2, shews that the value of 

 an annuity of £l. paid half-yearly, is the value of the same 

 annuity paid yearly + ^, and the value of an annuity of £1. 

 paid weekly, is the value of the same anniiity paid yearly 



H , the annuity being supposed to commence at the end of 



a year, and the first weekly payment to commence at the end 

 of a week. 



When the Table of moi'tality which is made use of gives 

 the deaths at every age, the preceding method can only be 

 considered as an approximation, but in all cases I believe the 

 error due to this method will be less than the error due to the 

 errors of the observations. 



The same series, p. 324, line 2, furnishes a method, which 

 I think is the simplest which can be proposed, of calculating 

 approximately the values of annuities or insurances on two or 

 three lives. 



The value of an insurance on one life, is easily deduced 

 from the value of the annuity; in fact, if A is the value of the 

 annuity, the value of the insurance in a single payment is 



and the value of the premium is 



ji {I +r) I +r 



When the persons observed upon whom the Table of mor- 

 tality is founded, are few in number, and the deaths are given 

 for every year, they will present considerable irregularities owing 

 partly to the effect of accidental causes, and partly to the un- 

 avoidable errors of the observations, but these causes may be 

 considered in theory as identical. If e, be the probability that 



