COMPOUND INTEREST.
17
c
•-o c/q
= mn
875,001 as before.
ivhen stocks are 90 :
the interest as it
nterest in the funds
06 = £8209 14 4
nds prevent us from
ant of an investment
as it is not probable
pnal rate ; it is there-
ic amount will be, to
b our calculation shall
f money being received
e of much importance
t out in this way for a
erable. The following
* interest of ¿Cl for one
session being expanded
and the remaining part
3 converges very fast, is
When in equals 2 the difference is —, when in equals 4 it becomes
3 i 2 i 3 i*
IT + l6 + 256*
27. The greater the number of intervals at which interest is payable,
. , m — 1 m— 2 . ,
the more nearly do , , &c. approximate to unity. If then
we write the limit unity for each of these fractions, we have the amount
of £l in one year on the supposition that there is no portion of time,
however small, but what produces some interest. The series then
V* Z a
becomes 1 + » + + YHTo +
+
:,&c., which
1.2.3.4 ' 1.2.3.4.5’
series, as shewn by writers on logarithms, is equal to the number that
has* for its Naperian logarithm, or i X .434294482 for its logarithm
in the common system.
Example. What will be the amount of £300 in one year at 4 per
cent, compound interest payable momently ?
p = 300
log
i — .04
1+ -
m
.434294482
.04
.01737177928 1.04081
[amount of £l
[ in one year.
300
When in is infinite, the formula ( 1 +
312.243= £312 4 10.
when expanded,becomes
+
i n'
:,-j-&c., which series
, L It t
* m 1 ^ 2 | j ^ i j ^ i ^ ^ 2 j ^}
is equal to the number that has in for its Naperian logarithm, or in
X .434294482 for its logarithm in the common system?
Example. What will be the amount of ¿£300 in 40 years at 5 per
cent compound interest payable momently ?
p — 300, i = .04, n ~ 40
.04
in — 1.6
.43429448
6.1 inverted
log { 1 +
43429448
26057669
69487117
4.95303
300
1485.909 —
28. In the first of these examples the amount of £l in one year, if
interest were payable yearly, would be 1.04; the difference between this
