Völkerrecht und Landesrecht

The nature of capital and income

Bibliographic data

Monograph

Identifikator:: 102659555X

URN:: urn:nbn:de:zbw-retromon-82920

Document type:: Monograph

Author:: Fisher, Irving http://d-nb.info/gnd/118533541

Title:: The nature of capital and income

Place of publication:: New York

Publisher:: The Macmillan Company

Year of publication:: 1923

Scope:: XXI, 427 Seiten

Digitisation:: 2019

Collection:: Economics Books

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Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Part III. Capital and income

Collection:: Economics Books

Sec. 5] CONCEPT OF RATE OF INTEREST 197 (1) If the rate of interest, in the sense of a premium on this year’s goods in terms of next year’s goods, is the same year after year forever, then the rate of interest considered as the price of capital in terms of a perpetual annuity will be equal to it. A numerical example will make this clear. We shall sup- pose that the rate of interest is four per cent in the premium sense, i.e. that $100 at any moment during the period under consideration will buy $104 to be paid one year later. We are to show that as a consequence $100 will necessarily buy an annuity of $4 a year forever. Let us suppose, then, the premium rate being 4 per cent, that $100 is spent for $104, to be repaid one year later. Of this $104, when it is received at the end of the year, the investor reinvests $100. By our hypothesis of an unchanged interest rate, this $100 will bring, at the end of the second year, another $104, of which in turn $100 is reinvested; and so on indefinitely. By continually reinvesting, he obtains for his original $100, $4 a year indefinitely and $100 deferred indefinitely. If the process is perpetual, the $100 is deferred to infinity, and has no present value. Hence the original $100 obtains simply a perpetual annuity of $4 a year, and the rate of in- terest in the price sense is therefore also 4 per cent, which was to have been proved.' Tt is evident that this reasoning may all be put in general terms, and that it applies equally to interest reckoned semi-annually, quarterly, ete., and continuously. : (2) Conversely, if a given rate of interest in the price sense holds good to-day, next year, two years later, and SO on indefinitely, then the rate of interest in the premium sense will be equal to it. This also may be readily shown by an example. If $100 will buy $4 a year forever, the first $4 being due one year ts in obtaining the present value of d adding the results. This process btaining the capital-value of a ! An alternative proof consis each successive item of income an is exemplified in the next chapter in 0 perpetual annuity.

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