FIRST APPROXIMATION

B. Principle of Repayment

All loans are repaid with interest, that is, the presentvalue of the payments, reckoned at the time of contract,equals the present value of the repayments. More gen-erally expressed, the plus and minus alterations or de-partures from a person’s original income stream effectedby buying and selling at two different points are suchthat the algebraic sum of their present values is zero.

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

These are really questions in mathematics. It is afundamental principle that in order to solve an equationcontaining only one unknown quantity only one equationis necessary; and that to solve one containing two un-knowns, two independent equations are needed; and soon, one additional equation for each additional unknownquantity introduced.

In the present problem we are trying to determine onlyone unknown, the rate of interest. But we can do so onlyby determining, at the same time, the other unknownsthat are involved. To say that the rate of interest is equalto Smith’s marginal rate of impatience is saying some-thing, but not enough. It merely expresses one unknown,the rate of interest, in terms of another unknown, Smith’smarginal rate; and two unknowns cannot be determinedby one equation or condition. If we add that the rate ofinterest must also equal Jones’ rate of impatience, whilethis statement gives us another equation it also adds an-other unknown and three unknowns cannot be determinedby two equations; and so on. If we include Jones and

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