CHAPTER IX

THIRD APPROXIMATION TO THE THEORY OFINTEREST

Assuming Income Uncertain

§1. More than One Rate of Interest

The great shortcoming of the first and second approxi-mations, from the standpoint of real life, is the completeruling out of uncertainty. This exclusion of the risk ele-ment was made in order to make the exposition simplerand to focus the reader’s attention on the factors mostrelevant to the theory of interest. But in real life the mostconspicuous characteristic of the future is in its uncer-tainty. Consequently, the introduction of the element ofchance, or risk, will at once endow our hypothetical pic-ture with the aspect of reality. The foundation for ourstudy of risk in relation to interest has already beenlaid in Chapter IV where the relation of risk to timepreference was noted.

One consequence of changing our assumption as to thecertainty of future events is to compel the abandonmentof the idea of a single rate of interest. Instead of a singlerate of interest, representing the rate of exchange betweenthis year and next year, we now find a great variety ofso-called interest rates. These rates vary because of risk,nature of security, services in addition to the loan itself,lack of free competition among lenders or borrowers,length of time the loan has to run, and other causes

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