Völkerrecht und Landesrecht

The nature of capital and income

Bibliographic data

Monograph

Identifikator:: 189206295X

URN:: urn:nbn:de:zbw-retromon-239471

Document type:: Monograph

Author:: Triepel, Heinrich http://d-nb.info/gnd/117417920

Title:: Völkerrecht und Landesrecht

Place of publication:: Tübingen

Publisher:: Mohr Siebeck

Year of publication:: 1907

Scope:: XII, 452 S.

Digitisation:: 2022

Collection:: Economics Books

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Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Erstes Kapitel. Völkerrecht und Landesrecht als Gegensätze

Collection:: Economics Books

Skc. 1] VALUE OF CAPITAL 203 of one year, the sum of $104, the present value of this right, if the rate of interest is 4 per cent, will be $100. If the property is the right to $1 one year hence, its present value is evidently 5; or $0.962, and if the sum to which the property entitles the owner is any other amount than $1, its present value is simply that amount divided by 1.04 or multiplied by .962. Thus the present value of $432 due in one year is ju, or 432 x .962, which is $416." If the future sum is due in two years, and the rate of interest is still 4 per cent, it is evident that $1 to-day is the present value of $1.04 next year, which in turn (by compounding) will then be the present value of $1.04 x 1.04 (i. e. [1.04] %, or $1.082) at the end of the second year. The $1.082 is called the “amount” of $1 at the end of two years, and $1.04 is the “amount” of $1 in one year. Similarly, in three years (1.04)° is the “amount” or sum worth $1 in present value; and so on for any number of years. These results show what $1 to-day is worth at the end of any number of years. And conversely, from them it is easy to see what $1 due at the end of any number of years is worth to-day. We have already seen that the present worth of $1 due in one year is fg or $0.962. Similarly, the present value of $1 due at the end of two, three, etc., years is respectively wig, ops etc.’ Knowing the present value of $1, we may evidently find that of any other sum by simple proportion. To illustrate these results geometrically, let us represent time by horizontal lines, and the value of the capital by vertical lines: then the curve 4 A” A” A’, as shown in Figure 1, will exhibit the relative values at any two in- stants, exchangeable on the basis of a given rate of interest, compounded annually. : , : The point B represents the present instant; B’, the in- ! For the general mathematical treatment, see Appendix to Chap, XIII, § 1. 2 For a mathematical formulation, see Appendix to Chap. XIII, § 2.

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