Remarks on the Principles of Compound Interest. 333 



a paradox so revolting to common sense. The fact is, that 

 the obviously greater value of an annuity beginning immedi- 

 ately, and payable hourly or daily at the option of the receiver, 

 is reduced, in their method of computation, by the virtual in- 

 crease of the discount, to the bare value of an equal annuity 

 of which the payments are all accumulated at the ends of the 

 respective years ; a change which certainly could not be a 

 matter of indifference either to the payer or to the receiver, 

 and neither of them " would have the least difficulty in deter- 

 mining which of the two Doctors he should prefer to follow," 

 though their deternmiations might be somewhat at variance. 



Dr. Young has not asserted that this difference is the same 

 in all cases of annuities; although he has taken for granted 

 that it is the same in annuities on lives as in perpetual an- 

 nuities, because the present value of the remotest possible pay- 

 ments is in both cases evanescent. 



The objector has certainly not understood the nature of the 

 argument by which Dr. Young has attempted to prove the in- 

 accuracy, or rather the impropriety, of Dr. Price's estimation 

 of the identity of the rate of interest. The tenor of that argu- 

 ment is, that when Dr. Price supposes he is reckoning on two 

 annuities at the same rate of interest, he is in fact employing 

 different rates : for that the discount on 10 shillings, receiv- 

 able at a certain moment, as a payment of the half-yearly an- 

 nuity, is greater, in the computation, than the discount on 1 

 shillings receivable at the same moment as half of an annual 

 payment; and therefore that the rate of interest cannot pro- 

 perly be called the same in the two cases. The objector makes 

 Dr. Young assert that the discount ought to be greater when 

 the payment is half-yearly ; which is quite a different ques- 

 tion, because this comparison relates to one half of the whole 

 number of half-yearly payments only. 



When the sense of an author is mistaken, it is easy to tri- 

 umph over the supposed absurdity of his conclusions : and in 

 this manner your correspondent has perfectly succeeded in 

 exposing the errors of those who do not understand Dr. Price's 

 solution ! With the greater part of his last paragraph, how- 

 ever, I fully agree, though many might be inclined to oppose 

 to him the high authority of Mr. Morgan, whose testimony, 

 though somewhat vague, seems greatly calculated " to en- 

 courage the popular delusion of the improved healthiness and 

 greater longevity of the people of this kingdom," which the 

 objector seems so much to deplore. 



Waterloo-place, 2d Oct. 182/. F- R- S. L. 



LVI. On 



