12 FOKF.ST VALUATION 



1. Fundamentally this series is: 



sum, S = a -j- ar -j- ar 2 + ar 3 + ar 4 

 and 



Sr ar + ar 2 -f ar 3 + ar 4 + ar 5 



subtracting the upper from the lower, 



Sr S ar 5 a 

 or 



S(r-i)=a(r 5 -i) 

 when 



a(r 5 -!) 

 : (r-i) 



since 5 is the number of terms in the series, or n, and this form is 

 perfectly general, it may be written : 



a (r n i) 



: 77^7T 



In this series a is the regular payment, and r is the ratio between 



ar 2 

 any two consecutive terms, as : ->=-= r. 



ar 



2. Applying this to the above case of a yearly or current ex- 

 pense of $500 at 3%. 



sum, S = 500 (i-03 49 ) + 500 (I.03 48 ) + +500 



S (1.03) = 500 (i.03 5 ) + 500 (i.03 49 ) -f etc + 500 (1.03) 



here 1.03 is the ratio, i. e., 



5oo(i.Q3 49 ) ._ 

 500 (I.03 48 ) ~ r ' 3 

 subtracting : 



S (1.031) =5oo(i.o3 50 i) 



SOP (I.03 50 i) 



(1.03 -i) 



By looking up I.O3 50 in the tables (see Appendix), the compu- 

 tation becomes perfectly simple and requires little time. 



3. Since this same process applies to any similar case it may 

 be written as a general formula : 



a(i.op n i) 

 1 d.op-i) 



which may be expressed: 



The sum of a series of payments a coming every year, contin- 

 ued for n years and compounded at p per cent. 



