INTEREST. 



If the principal, amount, 

 iven, to find the time ? 



given 



-\ a a , . 



j =r n , therefore, - being 

 [P P 



Theo. 4. Vdivided by r till nothing re- 

 I mains, the number of divi- 

 J sions will be n. 



It seldom happens, however, that it is 

 necessary to work questions relative to 

 compound interest by these rules, as very 

 extensive and accurate tables have been 

 published by Mr. John Smart and others, 

 which save much labour in such calcula- 

 tions, and are therefore generally resort- 

 ed to in practice. The principles on which 

 such tables are formed will appear from 

 what has been already said: thus, the 



and rate, are numbers in a table shewing the amount of; 

 I/, in any given number of years, are 

 merely the powers of 11. increased by its 

 interest for a year; that is, r, r*, r3, 7*, &c. 

 and the numbers contained in a table of 

 the present values of I/, to be received at 

 the end of a given number of years, are 11. 

 discounted for those years, or 11. divided 



by the powers of r, that is, -,-,y- f &c. 



Tables of this kind being usually con- 

 fined to six or eight places of decimals, 

 necessarily give the amount beyond the 

 first three or four years somewhat less than 

 the true amount, but the difference is so 

 small as to be of no importance in the pur- 

 poses to which they are usually applied. 



TABLE I. 



Showing the Sum to which I/. Principal will increase, at 5 per cent. Compound In- 

 terest, in any Number of Years not exceeding a Hundred. 



Ex. 1. What sum will 5001. increase 

 to in 21 years, if improved at 5 per cent, 

 compound interest ? 



1500 X 2.785962 =; 13921. 19s. 7$d. 

 Ex, 2. What sum, if improved at 5 

 per cent, compound interest, will accu- 

 mulate to a million in 50 years? 



The increase of an annuity, if forborne 

 for a given time, may be found by this 

 table, in the same manner as the amount 

 of a given sum ; for as each payment of 

 the annuity will become due at an equal 

 distance from the time in which it would 

 have been due, the amount of the first 

 payment must give that of each of the 

 succeeding ones. 



