The nature of capital and income

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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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382 NATURE OF CAPITAL AND INCOME § 10 (to Cm. XIII, § 7) Formula for a Bond when Interest is reckoned oftener than yearly The formula in the case of semi-annual income when in- terest is reckoned semi-annually is evidently,— which applies just after an interest payment; just before, it is evidently V+; and at intervening intervals it is this value discounted, or for practical purposes, the simple formula, V+at!, where V is the value taken after the last « interest” payment, and # the time elapsing since that date. For the case of continuous interest, if we let, as in the previous chapter, 3 represent continuous interest, we have,— PZ Y= 3 + a 4 which formula remains unchanged during the entire period of the bond. These various formule may, of course, be somewhat trans- formed and simplified for practical purposes. Moreover, they may all be transformed in terms of the various rates of interest. Some actuaries apparently prefer to use, as the in- terest rate, only the “effective” rate, i, which is what we call the “rate of interest reckoned annually.” The preceding formula, which employ the semi-annual, quarterly, and other forms of interest rates, may be transformed by substituting their values in terms of i, in accordance with the relations shown in Appendix to Chap. XII, § 2. § 11 (to Cm. XIII § 8) Formula for Capital-value of Any Series of Income Installments We may express, in general formule, the capital-value of any income stream, as follows: Let a,, a, a5 represent the successive installments of income accruing at various times dis-

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