The News-Herald. [volume] (Hillsboro, Highland Co., Ohio) 1886-1973, 1896-04-23
what Bonds Are Worth.
WASHINGTON, d. @.


a The recent issue of bonds by the nat.
4 ional government, and the discussions
4 = to what the bonds should be worth in
( tie market, have created an interest in
the subject and may make the following
comments on a problem recently pub.
lished in the NEws-HERALD Of sufficient
Interest to your readers to be presented
In your columns. The problem was in
3 teachers examination and read as fol.
lows: If the 3O.year government A per
cent. bonds be bought at Ill l 8, what
rate will they pay on the investment ?
suspect the examiners were trying
Y to test the teachers interest in current
/ events and their knowledge of the diff.
+. culties of the problem rather than they
expected the teachers to solve it. Even
BY simple interest it presents very in.
steresting problem, but the person who
buys the bonds and the government that
sells the bonds account compound inter.
est; and using compound interest know
of no way to solve the problem, except
by approximation. The reason some
thought the government should be given
the right to sell 80 bonds at par was that
the common people would not solve the
Sproblem of finding the rate on bond
bought at premium. The sale of the
bonds might have been more popular"
yet anyone wishing to invest in bonds
could have consulted his banker.
At q former issue of bonds Secretary
Carlisle had this problem to solve:
What premium must the government
receive on it's SD bonds due in ten years,
interest payable quarterly, SO as to pay
the buyer only 80 interest? Secretary
Carlisle said the bonds would have to
bring 1929, and this statement was
criticised in certain newspapers. Any
higher algebra has similar problem,
and this result can easily be shown to
be correct. Wentworth's Higher Al.
zebra, page 353). 1t can also be solved
by arithmetic. I will give solution,
leaving out the condition of the interest
being payable quarterly, as tables for
compound interest that are usually &C.
ceesible do not have the amounts for /
per cent. If the purchaser, when the
bond natures, received as much as he
paid fol it, instead Of only the par value,
It is evident he could pay $l66s for a
elOO bond bearing 5 per cent. and re.
:eive 8 per cent on his investment. At
ihe end of the ten years the government
Jays him $3.50 less than what he paid for
:, and this has to be taken into consid-
sration. The present worth of this for
,en years at three per cent. compound
interest, or 1868 divided by 1.3439l63S,
4 . $49.6062. Sligo minus $49.6O62 gives
nl7.06, the amount that would have to
4 )e paid for hundred dollar bond. The
blowing rule gives good method for
diving such problems:
Find the forborne value (the final
'alne) of an annuity (the annual interest
4 'aid on hundred dollar bond) for the
4 iven number of years and the desired
! ate per cent. add 500 dollars to the
4 uotient, and divide this sum by the
ompound amount of 81 for the given
ime and required rate. The explana.
ion OF the rule is very simple. In the
roblem given, the purchaser receives $5
lterest every year for ten years. The
forborne" value will give what this
annuity" will aggregate the purchaser
the end of the ten years, each annual
lterest being placed at compound inter.
4 1t when received. Besides this interest,
le government pays the purchaser at
iaturity the lace of the bond or 500,
hich added to the forborne value of the
inual interest will give the total
mount received by the purchaser from
te bonds at the end of the ten years
ivide this amount by the compound
! mount OF 81 for ten years at three per
mt. and you get the sum he must pay
r the bonds-or the sum which placed
compound interest for ten years would
mount to the same as what he receives
pm the bonds. The Farmers and
eaders' Bank recently bought some 30
lar bonds. They know what money is
prth to them. We will say per cent.
aey then had this problem to solve
hat interest will we receive on our in
stment if we buy at llls 4 per cent
3nd due in thirty years, interest pay.
tle quarterly and money being worth
~ cent? This problem can be solved
algebra by using logarithms, and 81
q cent. nearly is the answer. If the
5ter per cent. is not given, however,
I'd ID supposed to be the same as the
sired per cent. of interest, l know of
way to solve it, except by approxima
IN, and if there is direct, exact way
solve it would like to be enlightened.
. approximation / get $500 nearly, as
rate OF interest the government pays
the bonds bought by the Farmers
~ TVa6ora' RQnk aa tho ,nya.,n.a..