The nature of capital and income . Fig. 39. present value at time A of the value BE, at time B, is evi-dently AC, found by drawing the discount curve CE. There-fore the value of the terminable annuity is equal to AD - AC, 376 NATURE OF CAPITAL AND INCOME or DC, which is the total discount on BE; the amount bywhich it is, as Bohm-Bawerk says, diminished in time per-spective. Similarly, the capital-value of the annuity, taken at any timelater A (just after an installment of income), is equal to the. smaller sum GH. Thus the capital-value gradually decreasesin accordance with the distance of
The nature of capital and income . Fig. 39. present value at time A of the value BE, at time B, is evi-dently AC, found by drawing the discount curve CE. There-fore the value of the terminable annuity is equal to AD - AC, 376 NATURE OF CAPITAL AND INCOME or DC, which is the total discount on BE; the amount bywhich it is, as Bohm-Bawerk says, diminished in time per-spective. Similarly, the capital-value of the annuity, taken at any timelater A (just after an installment of income), is equal to the. smaller sum GH. Thus the capital-value gradually decreasesin accordance with the distance of the curve CE from theline DE. In this representation the discount curve was drawn throughE. If another is drawn through D it may be shown that EFis the amount of the terminable annuity, or its value at thetime it terminates, if we suppose that each individual item is putat interest from its date to the point of time B. This amount,EF, is called the total interest on that capital in that interval. In the same way, at any intermediate time just after an install-ment, GI will represent the value of the annuity concentratedat that point, and this value will consist of two parts, HG,which is the (discounted) value of the part subsequent to K,and MI, the (accumulated) value of the part preceding K. APPENDIX TO CHAPTER XIII 377 The decrease in capital-value of the annuity, which has beenrepresented by the approach of CE to the horizontal line DEabove it, is better represented, however, by inverting G
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