s. 
COMPOUND INTEREST. 
IS 
at to £395.0394 at 
. i = 1.05 
ears 
- 1 
garithms. 
thms of the principal 
from the number cor- 
is the interest of £ 1; 
amount at compound 
; 325 
.05 
705 = i 
100 
5 per cent. 
.'terly, &c. 
ible he shorter than a 
i to the principal as it 
rill evidently be greater 
than when interest is only payable yearly, £100 at 5 per cent, payable 
half-yearly, will amount at the end of six months to ¿£102 10; this 
new principal being again put out at interest for the next six months, 
will give £105 1 3, the amount of ¿£100 at the end of the year, w r hich, 
if interest were payable yearly, would be only £105. 
The interest in this case for the year is £5 1 3, from which it 
appears that where interest is payable at shorter intervals than a year, 
the expression rate per cent, denotes, not the interest of ¿£100 in a year, 
but the sum of which the same proportion must be taken to find the 
rate per cent for one interval, as each interval is of a year. 
Using the same notation as in art. 19, and calling m the number of 
intervals, we have 
1 + — ) the amount of ¿£l at the end of the 1st interval: reason- 
m J 
ing as in Art. 19 we find ^1 + do. of ¿£1 at the end of one year. 
i \ mn 
1 H— ) do. ¿£l 
mj 
n years. 
multiplying by p 
= p ( 1+ 0 
do, £p n years. 
by logarithms, log s = log p + mn x log 
Bide. Find the amount of £l at the end of the first interval, and 
raise it to a power equal to the product of the number of years and of 
intervals at which interest is payable in the year, and then multiply by 
the principal. 
Example. What will be the amount of ¿£325 1 9 in 25 years at 4 
per cent compound interest payable half-yearly ?j ; 
p = 325.0875, i = .04, n = 25, m = 2, .*. mn = 50 
and the formula becomes 325.0875 x (1.02) 50 < 
by art. 19, (1.02) 50 “ amount of ¿£l in 50 years at 2 per cent, payable 
yearly. 
Table 3, (1.02) 50 — 2.69158803 
5780.523 
8074764 
538318 
134579 
2153 
188 
13 
875,0015 = £875 0 0^