II. ARITHMETIC OF FOREST VALUATION 



a. General. 



A stand of timber fifty years old after planting may be worth 

 two hundred dollars per acre. If this stand is to remain and con- 

 tinue to grow until it is eighty years old, it is right for the owner 

 to ask at what rate is the stand, now fifty years old, growing, what 

 per cent is this growth on the two hundred dollars which the stand 

 is now worth, etc. 



Since the stand does not pay or give up any interest, the two 

 hundred dollars or the value of the fifty year old stand is evidently 

 like a capital out at interest, where the interest remains unpaid, but 

 is added to the capital every year. In other words, the stand of 

 timber grows like capital out at compound interest. 



If the owner wishes to know what this stand has cost to pro- 

 duce or grow to the age of fifty years he adds up the various items, 

 cost of planting, care and taxes during the fifty years, and the rent 

 on the land. The ten dollars per acre spent in planting have been out 

 for fifty years without drawing any interest, they have grown, there- 

 fore, at compound interest for fifty years. The expense of taxes 

 and care comes every year, the sum paid out the first year has been 

 out for forty-nine years, the sum paid the second year has been out 

 forty-eight years, etc., for none of this interest has been paid. 



If the owner wishes to forecast or estimate what this stand is 

 worth to him today if it is to continue to grow until it is eighty years 

 old, he must first decide that when eighty years old the stand will 

 bring, say, five hundred dollars per acre and then discount the five 

 hundred dollars to the present day, i. e., for thirty years. 



From this it is evident that forest valuation works a good deal 

 with the arithmetic of interest, with discount and with the summa- 

 tion of series, usually geometric series, the geometrical progressions 

 of many writers. 



The following are the more common forms of interest here. 1 



1 The elementary treatment of these simple problems in literal arithmetic 

 has been fully justified by fifteen years experience in University teaching. 

 The student will do well not only to go over this ground very thoroughly, 

 work out all formulae on paper and repeat often, but also to speak aloud 

 the true meaning of each formula and learn to state, as in geometry, exactly 

 what each formula means. 



