COMPOUND INTEREST. 
21 
;; s= 210.3 ,s = 690 
n = 15 
log s = 2.8388491 
log;; — 2.3228393 
60)0.5160098 
.0086002 
1.02= 1 + j 
; 4 
.02 
4 
.08 = interest of £l for one year. 
.08 x 100 = 8 percent. 
33. These equations might have been obtained more readily, if in the 
formula found when interest is convertible annually, the interest for one 
interval had been substituted for the annual interest, and the number 
of periods of conversion for the number of years : this will appear 
evident on examining the demonstration in Art. 19, where the amount 
of £l in one year is called (1 + ¿), and the amount of £l in n years 
is shown to be (1 -f- i) n ; these expressions do not depend upon the 
time being reckoned in years, for by adopting the same mode of reason 
ing, if (1 + i) represent the amount of £l at the expiration of any 
other portion of time, (1 —f- ¿) 3 would be the amount at the expiration 
of twice that period, and (1 + if 1 at the expiration of n times that 
period; in whatever way, therefore, we express the amount of £l for a 
term at the end of which interest is convertible; the amount at the 
end of any number of the same equal periods may be found by raising 
that amount to the power represented by the number of periods. 
When interest is convertible at m equal intervals in a year, there are 
7)i7i of these intervals in n years, and the amount of £l at the expira- 
tion of the first of them is 
J 
, the amount at the end of n years, or mn terms. 
gives 
34. When we are in possession of the proper tables, the amount 
of £l may be found by looking under the rate of interest produced by 
dividing the annual rate of interest by the number of times interest is 
convertible in one year, opposite to the number of years obtained by 
multiplying the periods of conversion in a year by the number of years ; 
if the annual rate of interest be 4 per cent, the amount of £30 in 12 
years when interest is payable half-yearly, is obtained by looking in the 
Table under 2 per cent, opposite 24 years, where we find 1.60843, 
which multiplied by 30, gives 48.2529 = the amount; the same sum 
for a similar term when the annual rate is 6 per cent, payable 3 times 
a year, by looking under 2 per cent, opposite 36 years, where we have 
2.03988, and multiplying by 30, gives 61.196 for the amount. 
If we have a table of the logarithms of the expression 
(