THE NEW THEORY OF INTEREST 685. good will have less value than the present services. Suppose, then, the life-time of a machine is four years, and that every year the machine gives off a value represented by 100,. the value of the machine, supposing that?the up, der-valuation of the future is 5 per cent. per year, will be 100?- 95'23+ 90?0+86?8 -- 372'31. Here we must be careful not to confuse 'wear and tear ' with interest. Wear and tear, it should be noted, is not the gradual depreciation of a good in the sense that it does its work worse as time goes on. Any horse-dealer will tell us that he takes depre- ciation off the youngest horse he hires out, although up to a cer- tain age they do their work better each year. Depreciation is allowed for in machinery, although the machine is supposed to do its.work as well in the last years of its life as in the first. In fact, Wendell Holmes' ' One-lZioss Shay' is really the type of the machine. The wear and tear fund, accordingly, is what the Ger- mans call Amortisation a life insurance of concrete capital: a sum set aside each year, not to patch up old machinery, but to replace the capital when worn out. It has thus this difference from physical wear and tear, which is more or less gradual all through: it is slow at first, and rapid in the later periods. All the phenomena will be seen by considering the life-time of a durable good similar to that mentioned above. In a year's time it will have thrown off a service worth 100, and the value of the good will now be the three years' service still contah?ed in it. But these three years' uses are each one year nearer the present, and are, therefore, increased correspondingly in value. The sum then does not begin with 95'23, ?as one zmight ?ashly assume, but with 100, and the total value is 100+ 95'23x?;?90'70? 285'93.? Comparing this with the value a year before (372'31- 285'93--86'38), we find that the first (annual) use of the good l?m?ounted to 100, while the full wear and tear amounts to only ?'?. Thus, after wear tear is fully allowed for, there remains a net interest of 13'627, and the cause, as before, is the maturing of the future uses con- .tained in the durable good by one stage. Following this further; ?n another vet?r ' the good is worth 100+ 95'23-- 195'23: the depre- cmtmn ?s ?(]'70, and the net ?nterest 9'30. At the beg?nmng of the last year the good is worth exactly the service it will render, 100: what the good has lost is 95'23, which, deducted from the service rendered, leaves 4'77 of net interest. Summing up the results, we find (1) that what a durable good loses each year is the? last service of the series that was contained in it at the beginning of the year, and (2) that, owing to the progression of time, this always leaves over a net interest ?'?.? ,.
