PRESENT VALUE OF SERIES 1 3 



Since this sum represents the vahie of all these payments at 

 the end of the period, it may be termed the end value of the series.^ 



500(i.03=>'^— I) 



Query : Is the sum the same whether it begins 



(1-03—1) 



in 1902 or in 1925, whether it begins in ten years from now, or has 

 run for fifteen years? 



d. Present Value of the Series. 



A farmer or forester may be able to get $500 rent per year 

 from a certain property. He may wish to know the value of twenty 

 years rent of this property with a view to raising money or selling 

 the twenty years' rent. 



I. The end value or sum of the twenty years' rent is found as 

 above and is expressed : 



sum or end value =: 



1.03 — I 



But what is the value of this sum today ? 

 Keeping in mind that 



and that Cn is the above sum or end value of the series : 



, r^ C20 500 (1.03'°— I ) 



present value, Co = s. = 7 — ^ — ^; IS 



1.03" (1.03 — 1)1.03'° 



Expressed in words : The present value of a series of payments 

 of $500 coming every year, continued twenty years, compounded 

 at 3% and discounted at the same per cent, the first payment coming 

 a year from now, in general, 



4. 1 r • a (i.op°— I 



present value of series ==7 r—, rr 



(i.op — I) (i.op°) 



2. Assuming that the above series nms for twenty years and 

 suppose that it has already run for seven years, what is its present 

 value ? Evidently the owner is seven years to the good, he does not 



' The student will do well to write these formulae exactly as he has 

 learned to develop them. The temptation is to write, for instance, 



a (i.op" — I 



S = -. This is correct, but it loses the connection, the student for- 



.op 

 gets how he came by it. In solving ordinary problems write out the general 

 formula and keep this before you. This will avoid many mistakes. 



