AGRICULTURAL ECONOMICS 



vailing premium on the present." If the net an- 

 nual income derived from a piece of land is three 

 dollars per acre and the rate of discount is five per 

 cent., the present capital value of the land would 

 be sixty dollars per acre. Sixty dollars, is, then, 

 the amount of money which, if lent at five per 

 cent, would yield an annual income of three dol- 

 lars. This is usually spoken of as the capital 

 value of the land. 



That this simple method of dividing the three 

 dollar net rent by the prevailing rate of discount 

 to find the capital value of a piece of land is 

 equivalent to finding the sum of an infinite series 

 of prospective net annual three dollar rents dis- 

 counted at the same rate may be demonstrated as 

 follows : 



The present value of a dollars due in t years 

 if the interest be compounded annually at the 



rate of r would be / \ \ t smce X dollars com- 

 pounded at rate r would give X (i-t-r)* 9 

 and HX(i+r)' = a then^T= /^y If then 

 the net income of a farm be a dollars a 

 year its value would be expressed by the 



equation: V = ~ + 



, . 4 + ad inf. This is an infinite "geo- 



metrical" progression with first term T and 



188 



