12 FORlvST VALUATION 



i. Fundamentally this series is: 



sum. S = a 4- ar -(- ar 2 -f- ar 3 -|- ar 4 

 and 



Sr ar -f ar -f ar 3 + ar 4 -f ar B 



subtracting the upper from the lower, 



Sr S ar 5 ~a 

 or 



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

 when 



c a(r s -i) 

 1 (r-i) 



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

 perfectly general, it may be written : 



(r-i) 



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.o3 49 ) -j- 500 (i.Q3 48 ) -f ........... +500 



S (1.03) = 500 (I.03 50 ) + 500 (i.03 49 ) -f etc ......... + 500 (1.03) 



here 1.03 is the ratio, i. e., 



500(1.03-)- 

 subtracting : 



S (1.03 i) =500 (i.o3 M i) 



500(1.03" O 

 (1.03-1) 



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" i) 

 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. 



