VALUE OF FARM LAND 



date is discounted at this prevailing rate, and so 

 it is for all the succeeding rents. The present 

 values of the succeeding future rents grow smaller 

 and smaller as the time one must wait for them 

 becomes greater and greater, until finally the rent 

 which is due at the end of an infinite period of 

 time would be infinitesimal. 



When the rate of discount is five per cent., for 

 example, the present valuation of a three dollar 

 rent which will be due in ten years is approxi- 

 mately one dollar and eighty- four cents ; the three 

 dollar rent which is due after twenty years has a 

 present valuation of about one dollar and twelve 

 cents; and the three dollar rent which is due in 

 forty years has a present value of about forty-two 

 cents. If this process of discounting future rents 

 be carried far enough the point would finally be 

 reached where the present value of the future rent 

 is too small to be taken into account. The pres- 

 ent value of the rent which is due after an infinite 

 number of years is infinitesimal. If the pres- 

 ent values of all these future rents be added to- 

 gether the sum would be the present capital value 

 of the land, or the amount of capital which, if 

 lent at a rate of five per cent, per annum would 

 yield the same income as the land is yielding at 

 the present time. 



The simple mathematical method of finding 

 this "sum" is to divide the annual value, that is 

 the net rent, by the rate which "reflects the pre- 



187 



