Sacramento daily record-union. [volume] (Sacramento [Calif.]) 1875-1891, 1884-08-16
EDUCATIONAL.
INTERESTING METHODS FOR COM.
PUTTING INTEREST,
Which Will be of Interest to all
Who Have Computations of
Interest, ETC., to Make.

| EDS. REcoRD-USIoY: In your paper of
! the Goth ultimo you reviewed at some
| length Professor Atkinson's book, Inter
est made Easy; a-Thousand Years as a
Day Short, Simple, Practical Method"
l have not seen the book, but shall regard
your comments on it as being correct.
The method of Professor Atkinson is not
new, nor, as stated by you, altogether cor
rect About thirty years ago Yankee
| schoolmaster, Alva Covington by name,
from Charlestown, Mass, came to the little
sleepy old town of Springfield, KY, and
founded seminary. He was the strictest
disciplinarian. the clearest- headed, most
modest, painstaking, kind hearted, and al.
| together the best school teacher that | ever
knew. He has gone the way of all the
earth; but on Cemetery hill, overlooking
the drowsy old town, more than thousand
men and women, once his scholars have
raised noble monument to his yet nobler
memory.
/ This master taught Us this rule: Every
principal is its own interest, at 6 per cent.
per annum, for log years, or 200 months,
!
was so. The first step was to make us I'M
derstand that 500 at 6 per cent. would earn
So in one year. This accomplished, our
way was made clear. The next question
was: If 500 at 6 per cent. will earn Sc in
one wear, how long wi | it take it to earn
itself, or 800? Obviously, as many years
as So are contained in 500, or 163 years.
Now, 1853 years are equal to 200 months, or
5000 days. That is, 200 months and
6000 days are equal periods of time. To
make myself clearer 200 months and 5000
days, each represent, are, i'll fact, 163
years, the precise time in which any sum
| of money will earn itself at 6per cent.
| They are divisible, without leaving frac
ton, by the simple process of removing the
decimal point to the left. They are multi
pliable, without producing a fraction, by
removing the decimal point to the right
Being absolutely equal, that condition re-
| mains unchanged whenever they are null
| tiplied or divided by the same number. In
dividing, if we move the decimal point, i'll
each, the same number of places to the left,
the quotients represent exactly the same
periods of time, The only difference
| is one is expressed in months and
the other in days. To divide 200 months
and 5000 days, respectively, by 10, we re-
move the decimal point one place TO the
| wv
DAYS, respectively, as quotients. Now, the
rule which l have given proceeds on the
| basis that every month contains 80 days,
neither more nor less. 1t is clear, then,
that 20 months are exactly equal to 800
DAYS. We remove the decimal point two
places to the left, and we have divided 200
months and 5000 days by 100. Our quo
tents of . months and 60 days stand for
precisely the same length of time. If We
| remove the decimal point three places to
the left, we have divided each by 1000. In
the one case we have 200-l000 months,
equal to 2-1O months, equal to days. In
| the other. the case of 5000 days, we have 6
DAYS. without fraction. The value of the
GO days quantity in the system is here
made plain 1t clears the most difficult
example in interest of all fractions of time !;
for if we should, in any case, be required to
calculate the interest for half a day, we
should do il by taking 1-12 OF the interest
for days.
Now, We treat the principal, the interest
of which we are required to find, in pre-
cisely the same manner that we have
treated the 200 months and the 5000 days
propositions Being its own interest, at 6
per cent, for 200 months or 6,0O0 days, ii
is 50 far as calculating interest is con-
cerned, 300 months and 5000 days, or
|
Suppose that we were required to find
the interest on s. ,2S3, at 4 per cent. yearly
for years, 3 months and % days.
The rule given proceeds on the assump-
ton that every month contains 80, and
every wear $50 days, and on that theory il
is fundamentally correct. The theory,
however, involves the loss of ; days in each
year 1t was this qualification of the rule
that our old master at Springfield took the
clcarest methods and the most pains to eX-
plain You do not notice ii III your obser-
vations on Professor Atkinson's book. II
the author has not taken it into account il
were best that he should. | hope that he
has done 50, for, but for the doubt OF 1t, |
should not trouble you with this writing.
The first step in the solution of our ex-
ample is to reduce the time-7 years,
months and 90 days, tn true time, of both
months and DAYS and OF days Disregard
ing the loss that occurs for > months, thai
for years. according to our rule, is % days
The following represents the true time
, 7 wears. > months and 81 days
, equal to, SIS months and % days
equal to 1858 days Our principa
is S7,2e300 Now, if we remove tho
decimal point one place to the left, We have
$72S. 800 the interest for 20 months Now
, in doing the sum, we never put thost
, figures down, but multiply them by /
mentally. and put down $2,913.200-thc in
: terest for 50 months. We move the deci
| NAL point two places to the left and We
: have So. SO O0-the interest for months
but we never put these figures on the SLATE
or blackboard. We multiply them, " il
! the mind" by and put down S29l.32.OO-
. the interest for eight months. Bat beior
= the pupil has put all the figures on thu
: board, he discovers that they represent JUS
l one-tenth of the sum he has Just written a
e the interest for so months And, RICH
here it should be stated that, where tn
time is less than POO months, if tn
interest for the largest number q
= even months be correctly found, tn
| calculation will be able To dcduCe, or calcu
V late. all the rest from it. We are now t
c find the interest for % days. Well, If "
=. move the decimal point three places to tn
|. left we have s. 800, the interest for 81
= DAYS. This we never write. but multipl
5 it, mentally, by i, and get 500 Il. 2O0--th
Il interest for a days. Here again the curl
t. usitv OF the learner is excited by the lac
: that the interest for "a days is just one
;. tenth of that for s months. In mOmeI
$ all is clear lie muitiplics months by 3
$ DAYS. mentally, and gets $40 days. In min
e cases out of ten he will perform some pre-
n cess of this kind without ever thinkn
a {;.bout removing the decimal point to fin
:, out what the interest for days Is. 1t re
/ mains to get the interest for days. Wei
j / DAYS are 0ne-sixth OF - days, therefor
e one-sixth of the interest, so. 200, for
/, DAYS. or $lS5.530, is the interest for day
IS The interest on S7,2S300 at 6 per cent. pc
$ annuIu for IS months and IS days, or fc
II 2.GGS DAYS, their equivalent, is the sum {
If these several amounts, or 50, 23S .50.11. Ont
.c sixth of the interest, at 6 per cent, or 500
st 1912. would be the interest on 81, $500 Il
d the given time ut per cent, and one-ha
he of the interest At l per cent, or S269.Si.,
&c would be the interest on 81 ,2S30O at on
is half of per cent. for the given time. I'll
a sum ofthe-sc three amounts, $4,O4S.l3.l4
or the interest on s., 2S3,00 at :! per cent
= wear for IS months and p days. or 90
is DAYS Keeping in mind the calculatic
cs jus; performed, the inverted comma oy,
% the principal, representing the division n
$ fectcd By the removal OF the decimal poin
ii and not putting the results of the ment
W work on paper, the figures actually require
g in doing the sum are rs follows:
rs Principal
of S7gss.SOO Interest
For ~ 1882
For months ....... --....-....- W -
~ For II ZgiI
= For days.............. ............... $50
Ut Interest for IS months and IS days, at
&C. per cent -, ~ ~
4 Interest Gt per cent. year........... j39 10
n Interest at one-half of per cent a