INTEREST. 



greater or less time ; while in the latter 

 the interest which becomes due in the 

 first year, or other interval, is added to 

 the principal, and thus forms a new capi- 

 tal, on which the interest of the second 

 year is to be computed ; and thus the ca- 

 pital, and consequently the amount of in- 

 terest, are continually increasing. Sim- 

 ple interest only is lawful in loans between 

 individuals, and in discounting notes or 

 bills of exchange ; but in the granting or 

 purchasing of annuities, either for terms 

 of years, or for lives, or of leases, or re- 

 versions, it is usual to allow the purchaser 

 compound interest for his money, unless 

 there is a particular agreement to the 

 contrary. 

 INTEREST, simple. If 51, is the interest 



of 1001. for a year, , or .05, is the in- 

 terest of II. for the same term : for, as 



100 : 5 : : 1 : -. Let then the interest 



100 



of I/, for one year = r; the principal = 

 p ; the time = t ; the amount in the 

 said time, viz. principal and interest = a. 

 Then r being the interest of II. for one 

 year, the interest of 11. for two years will 

 be 2 r ; for three years, 3 r ; and for any 

 number of years, t r. Now, as one pound 

 is to its interest, so is any given principal 

 to its interest, or 



As 1 : t r -.: p : p t r = interest of p. 

 Then the principal being added to its in- 

 terest, their sum will be == a, the amount 

 required ; which gives the following the- 

 orems for answering all questions relat- 

 ing to simple interest, viz. 



If principal, time, and rate, are given, 

 to find the amount. 



Theo. l.p t r-f-/=a. 



If the amount, time, and rate, are giv- 

 en, to find the principal ? 



Theo . 2 .__ =/ , 



If the principal, amount, and time, are 

 given, to find the rate ? 



Theo. 3. ^ = , 



If the principal, amount, and rate, are 

 given, to find the time ? 



Theo. 4.^=2-*. 

 pr 



Ex. 1. What sum will one penny 

 amount to in 1808 years, if put out to in- 

 terest at 5 per cent, per annum ? 



Multiply .004166 by 1808 and by .05, 

 the product is .376666, which, add- 

 ed to the principal, gives .380833 

 7s. 7\d. 



Ex. 2. What sum will amount to 100/. 

 in seven years, at 4 percent, per annum ? 



Multiply 7 by .04, and add 1, which 

 makes 1.28; divide 100/. by this 

 sum, and the quotient is 78.125 = 

 781. 2s. 6d. 



Ex. 3. At what rate per cent, per an- 

 num, will 1001. amount to 145/. 10*. in 7 

 years, at simple interest ? 



Subtract 1001. from 1451. 10s. the re- 

 mainder is 451. 10s. which, divided 

 by the product of the principal 

 and time, or 700, gives .065 = 6 

 per cent. 



Ex. 4. In what time will 1251. amount 

 to 212/. 10s. at simple interest of 5 per 

 cent, per annum ? 



Subtract 125/. from 212/. 10s. the re- 

 mainder is 87/. 10s. which, divided 

 by the product of the principal 

 and rate, or 6.25, gives the answer, 

 14 years. 



Tables of simple interest are easily 

 computed, and many such have been pub- 

 lished, but those only are of much utility, 

 which show readily the interest of any 

 sum for any number of days. Such a ta- 

 ble is unavoidably very extensive, and 

 forms of itself a thick volume; it cannot 

 therefore be inserted in a work of this 

 nature, but that which follows will answer 

 all useful purposes to those who are ac- 

 quainted with decimal arithmetic. Such 

 as prefer a table expressed in pounds, 

 shillings, and pence, are referred to the 

 interest tables published by Mr. John 

 Thompson of Edinburgh, Mr. Joseph 

 King of Liverpool, and particularly to the 

 improved interest tables of Mr. William 

 Reed, which show at one reference the 

 interest at 5 per cent, of all sums, at the 

 dates that usually occur in business. 



The interest of any sum, for one day, is 

 found by dividing the annual interest by 

 365; thus, at 5 per cent, the interest of 

 11. for one day is - - - - 00013699 

 which, multiplied by 2, gives 



the interest for 2 days - - 00027397 



by 3 - - 3 - - - 00041096 



by 4 - - 4 - - - 00054795 



and by proceeding in this manner, the 



following table is easily formed. 



