332 Remarks on the Principles of Compound Interest. 



free communication and tlie ultimate concentration of these 

 truths, we shall be conducted with slow, but with less erring 

 steps, to the more obscure and sublime parts of the system. 



LV. Remarks on the Principle of Compound Interest. In reply 

 to r. R. S. By A Correspondent. 



TF the interest of a hundred pounds for a day be a penny, it 

 -^ will be 365 pence for a year, according to the principles 

 of simple interest. 



But in all questions respecting pecuniary affairs extending 

 to many years, and in all transactions respecting annuities, it 

 becomes necessary to adopt the principle of compound inter- 

 est, which allows a repeated investment of the capital and in- 

 terest either yearly or monthly, or at shorter periods, without 

 any limit : although this principle can only be employed in com- 

 merce under particular restraints imposed by the laws of usury. 

 It is lawful, for instance, to receive ^^jl. in common years, 

 if not in leap years, each day that 100/. is in the hands of a 

 borrower : but at the end of the year, it is only lawful to re- 

 ceive 51. for the use of the lOOl. without any interest on the 

 interest. 



" Dr. Price and his followers " appear to consider the two 

 supposed transactions as regulated by the same rate of interest. 

 The sense in which Dr. Young has understood the " same 

 rate" comprehends the supposition of the possibility of laying 

 out the interest from day to day, to be improved at compound 

 interest ; by means of which the 5l. would receive an addition 

 of about half a year's simple interest on itself, or about half a 

 crown, at the end of the year : making a yearly interest of 

 about 5/. 25. Qd. ; which he considers as more correctly the 

 same rate with ^^-^l. a-day. If this is erroneous. Dr. Young 

 is in the wrong. 



It is allowable to use the word same in either sense, pro- 

 vided that the definition be borne in mind : but when the de- 

 finition is forgotten, the confusion may lead to errors in prac- 

 tice. It has been asserted, for instance, that the value of a 

 perpetual annuity payable yearly is exactly equal to that of 

 the same annual sum supposed to be paid " momently " in 

 equal portions : because this result is obtained by supposing 

 the annual interest to be divided through the moments, ac- 

 cording to the principle of simple and not of compound in- 

 terest : and in this manner mathematicians, even of deserved re- 

 putation, have been able to convince themselves of the truth of 



a paradox 



