58 FOREST VALUATION 



The sum of present or discounted values of rentals forms such 

 a descending series. 



These formulae apply either to temporary rentals, with a 

 limited number of terms, or to perpetual rentals, with an infinite 

 number of terms. 



For an in finite increasing series 



Q = s( f - = x (infinity). (Q,) 



q - i 



For an infinite decreasing series, since the value of $* dimin- 

 ishes in direct proportion to the exponent used, 



f =o. 

 Therefore 



81. Present, Expectation, or Capital Value of Temporary 



Annual Rentals. Let R = present, expectation, or capital 

 value of the sum of a rental. 



Should each rental be discounted to the present by Formula 

 I, the sum of the reuniting terms is 



i.op i.op 2 ' i.op 3 ' i.op*' 



Applying Formula Q. for the summation of decreasing 

 temporary rentals. 



,., i.op i.op 1 



K = * . 



i.op 

 Multiplying numerator and denominator by i.op X 



R = rd.op* - i) 

 (i.op i) i.op* 



o.op X i.op* 



(iv) 



