Elementary arithmetic, with brief notices of its history... by Robert Potts.

6
when it is due, but is added to the principal, so that the first year's
amount becomes the principal for the second year; and so on for the
third and the succeeding years.1
The compound interest of any sum for any number of years
may be calculated by proportion, for each successive year, as simple
interest.
1In finding the compound interest for any part or parts of a year after the expiration of several years, it is usual, for instance, if the compound interest be
required for 4i years, to take three-fourths of the 5th year's interest. This may be
objected to as implying that the interest is payable quarterly. This approximation,
however, does not differ much from the exact truth, as will be seen in the following
example.
To find the compound interest of ~300 for 4` years at 5 per cent. per annlum.
~
Y - U 300=First year's Principal.
15,, Interest.
-L 315,, Amount, or 2nd year's Principal.
15'75 Second year's Interest.
2o 330-75,, Amount.
16-5375 Third year's Interest.
i 317'2875=,, Amount.
17'364375 Fourth year's Interest.
jo 364-651875=,, Amount.
18 23259375 Fifth year's Interest.
13'6744453125 = - of 5th year's Interest.
364'651875 = Fourth year's Amount.
~378'3263203125=4] year's Amount.
20
s.6'5264062500
12
d. 6 31687500
4
q. 1 267500
~ s. d.
378 6 6~:=Amount.
300 0 0 =Principal.
~78 6 61-=Compound Interest for 4- years.
It may be here remarked that the number of decimal places in this computation might be restricted to 6 or 7, without incurring the error of a farthing.
If the compound interest of ~300 for 4-* years, at 5 per cent. per annum, be calculated from the formula M =P(l+r)", by means of a table of logarithms calculated
to seven places of decimals, it appears from the calculation that the correct result is,
~ s. d.
378 4 10 =Amount.
300 0 0 =Principal.
~78 4 10= -Compound interest for 4 years,
And the approximation is too great by Is. 8d. nearly.