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.

: l have not seen the book, but shall regard
: your comments on it as being correct.
j The method of Professor Atkinson is not
I 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
5 disciplinarian the clearest-headed. most
2 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 a thousand
men and women, once his scholars, have
raised q noble monument to his vet nobler
memory.
This master taught Us this rule: Every
principal is its own interest, at per cent
per annum, for log years, or 200 months,
or 5000 days. He explained to us why this
was so. The first step was to make us I'M
derstand that 500 at 8 per cent. would earn
S. in one year. This accomplished, our
way was made clear The next question
was: If 500 at per cent. will earn Sc in
one year, how long wi it take it to earn
itself, or 800? Obviously, as many wears
as So are contained in 500, or 16S years.
Now, 16S 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, III fact, 163
years the precise time in which any sum
of money will earn itself at 6 per cent.
They are divisible, without leaving a 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, in
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
left We then have 20 months and 600
days, respectively, as quotients. Now, the
rule which | 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
! =
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 200-1000 months,
| equal to 210 months, equal to days. In
the other, the case of 5000 days, we have
days, without fraction. The value of the
GOO 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 it 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
per cent, for 200 months or 6,000 days, it
is, so far as calculating interest is con-
cerned, 200 months and 5000 days. or
either, INTERCHANGEABLE.
| Suppose that we were required to find |
the interest on 81 ,2S3, at = per cent yearly |
| for years 3 months and % days
| The rule given proceeds on the assump- |
ton that every month contains 80, and |
! every year $50 days, and on that theory it |
| is automatically 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 |
clearest methods and the most pains to eX-
plain. You do not notice it in your obser-
yations on Professor AtkinsOn's book. If |
the author has not taken it into account, it
were best that he should. l hope that he
has done 50, for, but for the doubt of it, | |
should not trouble you with this writing.
The first step in the solution of our ex- /
ample is to reduce the time-7 years, 3 |
months and % days to true time, Of both |
months and days and OF days. Disregard
ing the loss that occurs for ; months, that |
for years, according to our rule, is - days.
The following represents the true time:
equal to, IS months and % days. |
equal to 2,G68 days Our principal |
is $7,2S300 Now, if we remove the
decimal point one place to the left We have
$I2S.30.0, the interest for 20 months. Now,
in doing the sum, we never put those
figures down, but multiply them by 1,
mentally and put down $2,913.2 00-the in
terest for 50 months. We move the deci-
NAL point two places to the left and we
have $72. 81. 0O-the interest for > months
but we never put these figures on the slate
or blackboard. We multiply them, in
the mind, by aud put down $29l 1890
the interest for eight months. Bat before
the pupil has put all the figures on the
board, he discovers that they represent just
one-tenth of the sum he has just written as
the interest for so months. And, right
here, it should be stated that, where the
time is less than POO months, if the
interest for the largest number Of
even months be correctly found, the
calculation will be able to dcduce, or calcu-
late, all the rest from it. We are now to
find the interest for % days. Well, if We
move the decimal point three places to the
left we have s. IS 800, the interest for six
days. This we never write, but multiply |
II, mentally, by J. and get 500 .200--thc
interest for n days. Here again the curl
osity OF the learner is excited by the fact
that the interest for "a days is just one
tenth Of that for s months. In moment
all is clear. lie muitiplics months by 30
DAYS mentally, and gets 30 days. In nine
cases ont of ten he will perform some pro
cess Of this kind without ever thinking
about removing the decimal point to find
out what the interest for 6 days is. 1t re-
mains to get the interest for days Well,
DAYS are one-siXth of 81 days, therefore
one-siXth Of the interest, so Is. 200, for a
days or Sl.S5.530 is the interest for days.
The interest on S7,2S30O at per cent. per
annum for IS months and 2S days, or for
2,6GS DAYS, their equivalent, is the sum of
these several amounts, or s. 23S. 80. -. One
sixth of the interest, at 6 per cent, or $3.50.
1912. would he the interest on s., 2S3.00 for
thc given time ut per cent, and one-half
of The interest at per cent, or S269.S1.56
would be the interest on y ,2S3.00 at one
half of per cent for the given time. The
sum oftht-ic three amounts, 81, 0fS. 1914, is |
the interest on s., 2S300 at y per cent 4
year for IS months and > days. or 2GGS
DAYS Keeping in mind the calculation
just performed, the inverted comma over
the principal, representing the division at
footed by- tho TpippVal of he decimal r,oiuf