[文献] 150论坛币！！资料求助！the nature of capital and income [推广有奖]

11楼

1253197054 发表于 2011-9-13 12:57:37

millton 发表于 2011-9-13 12:37
我怎么能给你随便复制粘贴的东西呢。那是从那个网页上复制后粘贴的。可以给你那个网页版的。楼主表要天忽 ...

milton 您让俺很为难哇！分明是你付出了劳动，但却是不符合要求。假如说内容是真实的，那么在俺不适应网上浏览的情况下，打印出来还是要花费很多代价的。然而在资料难以寻获的前提下，似乎应该知足……这样子吧，等到符合要求的资料出现后，我付给你50金币.（你卖个空文档，到时等与资料一起购买）不知兄台意下如何？

hello，hawaii

12楼

1253197054 发表于 2011-9-13 13:03:50

millton 发表于 2011-9-13 12:37
我怎么能给你随便复制粘贴的东西呢。那是从那个网页上复制后粘贴的。可以给你那个网页版的。楼主表要天忽 ...

兄台，实在没法看啊

hello，hawaii

13楼

1253197054 发表于 2011-9-13 13:05:39

millton 发表于 2011-9-13 12:37
我怎么能给你随便复制粘贴的东西呢。那是从那个网页上复制后粘贴的。可以给你那个网页版的。楼主表要天忽 ...

出现及其大量的乱码！！
APPENDIX TO CHAPTER XII 363

$ 100 will to-day buy the right to $ 4 a year forever, and a
year hence this right to $4 annually may be sold on a 3%
basis. It will therefore fetch $133.33. The investor will
consequently receive in all, at the end of this first year, a total
of $4-}- 1331, or $137i. Hence the rate of interest in the
sense of a premium will be for that year 37^%. In succeed-
ing years the rate of interest, considered either as a premium or
a price, will evidently be 3%.

5 (TO CH. XII, 6)

Mathematical Relations between the Rates of Interest as a Premium and

as a Price

In general, if we let i\ represent the rate of interest in the
premium sense for this year, i 2 for next year, i 3 for the third
year, and so on, whereas ji,j& and j s , etc., represent the
rates of interest in the price sense for the same successive
years, the following relations between the i's and fa may be
proved :

.ad inf.

' ' ' ad mf-

... ad inf.
-M* (1-M*)U + ^) (l + ^Hl + ^Hl-M*)

etc.

These equations may be said to determine j l} as a peculiar
sort of mean of the magnitudes i l} i z , i s , . . . ad inf., and j 2 as a
similar mean of i< 2 , i s , i' 4 , ... ad inf., etc. Their proof,
which is simple, is left to those readers who are interested in
mathematics.

The preceding equations express the values of the fa in

364 NATURE OF CAPITAL AND INCOME

terms of I's. The following equations give the i's in terms of
the fa :

Ji

etc.

Thus if, as in our example, J, = .04 and j 2 .03,

The proof of these formulae is also left to the mathematical
reader. He will observe that the two sets of equations may be
proved independently or either set may be proved and the
other set derived from it. To show that either set may be de-
rived from the other, it will be found useful to substitute for
the left-hand members of the first set their simpler values as

derived by algebra. These are, -,-,-, etc. An easy proof of

ji h h
this is found by actually dividing 1 by j^ etc.

From the formulae it is clear that if ij = * 2 = 3 =, etc., then
j l= j 2 =j s =:, etc., and that then all the i's = the fa. The
converse is also evident.

6 (TO CH. XII, 7)
Mathematical Relations between the Rates of Interest and Discount

Let V, due one year hence, be the equivalent of V available
in the present. Then the rates of interest and discount are
expressed respectively by the formulae :

Whence, by multiplying the two equations together we
derive (1 + i) (1 d) = 1, which reduces to d = i id. That
is, the number representing the rate of discount equals the
number representing the equivalent rate of interest less a

APPENDIX TO CHAPTER XII 365

small correction, equal to the product of the rates of interest
and discount.

The relation between the rates of discount and interest
when semi-annually reckoned is analogous to the relation which
we found between those annually reckoned. We then have

V d'

the equations, = 1 -

V i'

and = l ~

whence

By multiplication and reduction,

d'-i'-^

2 '

We may apply similar reasoning to quarterly-reckoned
interest and discount rates.

It follows that (l + j Vl - ^\ = 1

or

4

The same reasoning may obviously be applied to reckonings
n times a year. We then find,

j(.n)fj (n)
(jfr) -JO*)-* * .

n
It is evident that if n, the number of parts into which the

year is divided, be sufficiently increased, the term - - be-

n

hello，hawaii