THE THEORY OF INTEREST

present hypothesis, can be very easily remedied. Forinstance, he may lend some of the proceeds of its earlieroutput and in later years be paid back with interest.

Of course, his loan at five per cent does not alter in theleast the figure $9110, the discounted value at five percent of all the ten items of income ($2000, $1800, $1600,$1400, $1200, $1000, $800, $600, $400, $200); it simplyadds to the later of these ten figures and subtracts fromthe earlier ones. The present value of the additions isnecessarily equal to the present value of the subtractions;for the additions are the repayments, while the subtrac-tions are the loans, and the present value of any loanequals that of its repayment.

We may totally separate, therefore, in thought the twochoices made by the land owner, namely, (1) the choiceof C (mining) in preference to A and B on the groundof greater present value, and, (2) the choice of timeshape. If, as just supposed for illustration, the secondsort of choice is that of an even income stream, it willbe at the rate of $455.50 a year perpetually. That is tosay, the mine owner will lend at interest $1544.50 the firstyear (all but $455.50 out of his original mining income of$2000); in the second year he will lend $1344.50 (all but$455.50 out of his original $1800); and so on. When theninth year is reached, he ceases to lend further, for themine then yields only $400. Instead, he then ekes this outby $55.50 returned from the previous loans. Likewise, inthe tenth year he ekes out the $200 from mining by$255.50 returned from loans. Thereafter he will get noth-ing further from mining; but his loans will have accumu-lated a sinking fund (of $9110) to take the place of themine and from this fund he can annually derive a 5 percent revenue of $455.50.

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