294- " Dr. Price and his Followers." 



restraints on usury as an essential step in his calculations." 

 Where does this appear ? or what connection have those re- 

 straints with any calculations of the kind ? I am certain that 

 no such idea ever entered into the mind of Dr. Price, or of 

 any person acquainted either with the doctrine of annuities or 

 with the laws of this country. In order, however, to remove 

 all difficulties and correct all eiTors on the subject, we are 

 favoured with a much simpler process. " An annuity of \l. 

 payable half-yearly (is said) to be equal to two annuities of 

 ^ — the one beginning at the end of the year — the other anti- 

 cipated by half a year; and the value of this portion is greater 

 than the other by half of the payment, that is by ^" if the 

 annuity is payable quarterly, the excess will be \ the payment, 

 ov ^•, or in other words, the excess in the first case will be 

 ^ year's purchase of the annuity ; and in the second case it 

 will be 5 year's purchase ; nor does it appear to make any 

 difference whether the annuity be for life or a term, or whether 

 the term be 5 or 50 years — or whether the rate of interest be 

 4 or 40 per cent, so that in all cases an annuity of 100/. worth 

 1000/. payable yearly, will be worth 1025/. if paid half-yearly, 

 and 1012/. 10s. if paid quarterly. This is really setting all 

 the rules of arithmetic at defiance, and requires no answer. 

 By this indiscriminate mode of making the same additions to 

 all annuities, it is admitted that the calculations in some in- 

 stances become in appearance a little paradoxical ; for the value 

 of a reversionary annuity during one life after another, by 

 making the same addition to the single as to the joint lives, 

 becomes the same whether the payments are made yearly, 

 half-yearly, or at shorter intervals : but it is well known that 

 the additions to single and joint lives are different, and there- 

 fore that the values of all annuities in which single and joint 

 lives are concerned must vary as the payments are more or 

 less frequent. 



But I shall proceed no further with this subject, my motive 

 in entering upon it having been to prove the truth of Dr. 

 Price's solutions, rather than to expose the errors of those 

 who do not understand them. 



The public have lately been overwhelmed with tables of the 

 deci'ements of human life, formed either by amalgamating all 



payment is always greater : and it may be further proved, that the diflfer- 

 ence between the values in the former case is always less than it is in the 



latter. In other words, that in any given year («) the excess of 



\ + r\ 



above — is less than the excess of - — — — above 



