B. Principle of Repayment

All loans are repaid with interest, that is, the present value of the payments, reckoned at the time of contract, equals the present value of the repayments. More generally expressed, the plus and minus alterations or departures from a person's original income stream effected by buying and selling at two different points are such that the algebraic sum of their present values is zero.

Will these four sets of conditions determine the rate of interest? And why should there be so many conditions? Ought not one single condition to suffice?

These are really questions in mathematics. It is a fundamental principle that in order to solve an equation containing only one unknown quantity only one equation is necessary; and that to solve one containing two unknowns, two independent equations are needed; and so on, one additional equation for each additional unknown quantity introduced.

In the present problem we are trying to determine only one unknown, the rate of interest. But we can do so only by determining, at the same time, the other unknowns that are involved. To say that the rate of interest is equal to Smith's marginal rate of impatience is saying something, but not enough. It merely expresses one unknown, the rate of interest, in terms of another unknown, Smith's marginal rate; and two unknowns cannot be determined by one equation or condition. If we add that the rate of interest must also equal Jones' rate of impatience, while this statement gives us another equation it also adds another unknown and three unknowns cannot be determined by two equations; and so on. If we include Jones and Edition: current; Page: [124] everybody else in the market, we shall still be one equation short. This is equivalent to saying that the second set of conditions (Impatience Principle B) is not enough.

In a market comprising 1000 persons there will be, as our unknowns, not only the rate of interest, but 1000 rates of impatience, and the additions to or deductions from the income of these 1000 persons in each period of time. The rate of interest and these thousands of variables act and react on each other and the determination of each can be accomplished only with the determination of all the rest.

In Chapter XII this problem is stated in mathematical formulas such that the number of equations is exactly equal to the number of unknown quantities.

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