14 FOREST VAT,UATION 



need to discount it for twenty years but only for twenty less seven 

 or thirteen, and the case may be written: 



^ , 500(1.03^—1) 

 present value = 



(1.03-1)1.03"-' 



500 (1.03°°- i) 1.03" 



or = — ; ^ :z — 



(1.03— I ) 1.03=" 



this latter having the advantage that it keeps the whole story clearly 

 before the student. 



If in the above case the series does not begin until fifteen years 

 from today, evidently the discount to present time must be longer 

 by these fifteen years, and the case may be written : 



^ , .soo (los"*- i) 



present value = —, ^ rrnr 



( 1-03—1) 1.03""*" 

 or to make it more clear, 



500(1.03"- 1 ) 



-(1.03- 1) (1.03=") (1.03") 



e. Series of Periodic Payments. 



If a forest property can be cut over every fifteen years and at 

 each return the cut nets $500 it may become of interest to determine 

 what the value of ten cuts of the forest is. Assuming that the 

 property has just been cut over so that the next cut comes in fifteen 

 years and the last cut in one hundred and fifty years, the end value 

 or the value of the sum of these cuts is : 



I. End value or sum : 



S = 500 (1.03'=°-") + 500 (1.03""°) 500 



S (1.03") = soo (1.03''") + 500 (1.03^=°-") 500 (1.03") 



(Note that the ratio here is 1.03^^.) 

 Subtracting : 



S(i.03'»- I) =500(1.03""-!) 



^ 500 (1.03'°°- i) 



^- (1.03"- 1) 



If in the above case we let fifteen years = t, and 10, the num- 

 ber of cuts = n, then 150 = nt, and we may write the general form: 



a(i.op°'— I) 

 ^- (i.op'-i) 



Note: The student will recognize these periodic cases by the 

 exponent t in the denominator. 



