The nature of capital and income . his 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 (
The nature of capital and income . his 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 GE tothe position KB, in order that the capital-value may be repre-sented, as in our previous examples, by the distance from the. Fig. 41. horizontal line AB below it. This change is accomplishedin Figure 40. The value of the annuity taken after eachinstallment of income is represented by the ordinate, as mA,of the curve KB, and the value just before an installmentis represented by the ordinate, as nA, of a point above thiscurve a distance equal to that installment. The value at inter-mediate points evidently follows a discount curve, as mn, be-tween these two points. The result is that the capital-valuewill rise and fall according to the steps, or teeth, shown in thediagram. As the income items become more numerous the teeth be-come more frequent and smaller, and disappear when the flowof income is continuous, as represented in Figure 41, where the 378 NATURE OF CAPITAL AND INCOME curve KB itself represents the capital-value at all points ottime. The formula for the present value (F) of the annuity justafter each installment of income is the same, whatever thetime intervals be
Size: 1740px × 1436px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1910, bookpublisherlondonmacmillancol
