INTEREST. 
yearly, or quarterly, and is distinguished in- 
to simple interest and compound interest ; the 
former being merely the compensation paid 
for the use of a capital, at a certain fixed 
rate for a year, and a proportionately greater 
or less sum for a 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 capital, and 
consequently the amount of interest, are 
continually increasing. Simple interest oidy 
is lawful in loans between individuals, and 
in discounting notes or bills of exchange ; 
but in the granting or purchasing of annui- 
ties, either for terms of years or for lives, 
or of leases, or reversions, it is usual to al- 
low the purchaser compound interest for 
his money, unless there is a particular agree- 
ment to the contrary. 
Interest, simple. If 51. is the interest 
5 
of 1001. for a year, — or .05, is the in- 
terest of 11. for the same term: for, as 
100 : 5 :: 1 
_5_ 
' 100 ' 
Let then the interest of 
11. for one year = r ; the principal z= p; the 
time = 1; the amount in the said time, viz. 
principal and interest — a. Then r being 
the interest of 11. for one year, the interest 
of ll. for two years will be 2r; for three 
years, o 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 : tr :: p : ptr — interest of p. 
Then the principal being added to its inte- 
rest, their sum will be = a, the amount re- 
quired ; which gives the following theorems 
for answering all questions relating to simple 
interest, viz. 
If principal, time, and rate, are given to 
find the amount. 
Theo. 1. ptr-\-p = a. 
If the amount, time, and rate are given, 
to find the principal ? 
Theo. 2. t ^ fl = P 
If the principal, amount, and time, are 
given to find the rate ? 
Theo. 3. a -~ = r 
pt 
If the principal, amount, and rate, are 
given to find the time ? 
a — v 
Theo. 4. - ~ t 
pr 
J x. i. What sum w ill one penny amount 
to in 1808 years, if put out to interest at 
5 per cent, per annum ? 
Multiply .004166 by 1808 and by .05, 
the product is .376666, which added 
to the principal, gives .380833 = 
7s. 7\d. 
Ex. 2. What sum will amount to 1001. in 
seven years, at 4 per cent, per annum? 
Multiply 7 by .04 and add 1, which 
makes 1.28 ; divide 1001. by this 
sum, and the quotient is 78.125 = 
78 1. 2s. 6 d. 
Ex. 3. At what rate percent, per annum, 
will 1001. amount to 1451. 10s. 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 
2121. 10s. at simple interest of 5 per cent, 
per annum ? 
Subtract 1251. from 212 1. 10s. the re- 
mainder is 871. 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 com- 
puted, and many such have been published, 
but those only are of much utility which 
shew readily the interest of any sum for any 
number of days. Such a table is unavoid- 
ably very extensive, and forms of itself a 
thick volume ; it cannot therefore be in- 
serted in a work of this nature, but that 
which follows will answer all useful pur- 
poses to those who are acquainted with de- 
cimal arithmetic. Such as prefer a table 
expressed in pounds, shillings, and pence, 
are referred to the interest tables published 
by Mr. John Thomson of Edinburgh, Mr. 
Joseph King of Liverpool, and particularly 
to the improved interest tables of Mr. Wil- 
liam Reed, which shew 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 ll. 
for one day is 00013699 
which multiplied by 2 gives the 
interest for 2 days 00027397 
by 3 3 days 00041096 
by 4 4 00054795 
and by proceeding in this manner, the fol- 
lowing table is easily formed. 
