12 FOKKST VALUATION 



1. Fundamentally this series is: 



sum, S = a + ar + ar + ar' + ar' 

 and 



Sr = ar + ar + ar' + ar' + ar' 



subtracting the upper from the lower, 



Sr — S = ar° — a 

 or 



S(r-I)=a(r»-I) 

 when 



^ a(r'-i) 

 ''- (r-i) 



since s 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" 

 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 (1.03") + 50Q (1.03*') + +500 



S (1.03) = 500 (1.03"°) + 500 (i.os'") -f etc + 500 (1.03) 



here 1.03 is the ratio, i. e., 



500 (i.o.r) 

 subtracting : 



^ 1,03 

 500 (1.03'') 



S(i.o3 — i)=5oo(i.o3'»— I) 



g_ 5oo (1.03°"— I ) 

 ~ (1.03— i) 



By looking up 1.03"" 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) 

 (i.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. 



