COMPOUND INTEREST FORMULA 439 



the formulae usually adopted in scientific forestry investiga- 

 tions : 



Let a = present contents of the crop 



A = former contents 



n = the number of years between the two measurements 



p = the rate per cent, yielded. 

 Hence, the increment = a- A 



and the average annual increment = a ~ . 



n 



Now, if n be only I year, 



loo :p :: A : a- A 

 ..'. t- *= x :oo 

 and a = Ax i-op. 



But, if n is for a greater period than i year, 

 a = A x i-op n 



This formula will give the true rate of compound interest 

 But it is not very readily applicable for ordinary use. 



It may, however, be simplified with results approximately 

 correct by expressing the per cent, as equal to the per cent. 

 that the average annual increment for the period bears to the 

 mean contents during that period. 



Now, the mean contents are a 



and the average increment 



n 



Hence : 







a-A 



loo a + 



2 



I00 x Z x 



n + A 



a- A. 200 

 _ . 



n 



