FORMULA OF COMPOUND INTEREST 57 



Since i.op i = o.op, 



Fr _r(..or-.) 



o.op 



'-(i-op n - i). 

 o.op 



Outlay for fire protection or sums paid annually for adminis- 

 tration serve as examples of annual rentals. As income we may 

 have receipts from grazing or hunting privileges. The above 

 formula holds good only during the period that such rentals 

 remain equal in amount and value as is the case with actual 

 rent. Should they fluctuate annually, each item must be sep- 

 arately computed. 



If rentals remain the same for a period and then rise or fall 

 to a different level for a second period, the above formula is 

 used to compute the total to the end of the first period. This 

 value then bears interest for the remaining period as a definite 

 sum (I), and the value of the new rental r\ for this second 

 period is computed in the same manner as before and added to 

 the total. For two periods termed a and b this reads: 



_ 



o.op ) o.op 



80. Formulae for Geometric Series. In the series whose sum 

 is obtained by Formula III, the ratio i.op is greater than i, 

 which gives an increasing series. 

 Let g = first term of series. 



q = ratio or multiple (such as i.op). 

 Q = sum of series. 

 Then, by demonstration above (III), 



The sum of future values of rentals forms such a series. 



Should the ratio be less than i, each succeeding term will be 

 diminished in value, which gives a decreasing series. 



The sum of this series is obtained by the same formula, but 

 a more convenient form of expression, obtained by multiplying 

 both numerator and denominator by i , is 



(Q,) 



