PRESENT VALUE OF SERIES 13 



Since this sum represents the value of all these payments at 

 the end of the period, it may be termed the end value of the series. 3 



500 (i.o3 50 i) 



Query : Is the sum - - the same whether it begins 



(1.031) 



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 : 



500(1.03" i) 



sum or end value =: - 

 1.031 



But what is the value of this sum today? 

 Keeping in mind that 



-i.op n 

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



CM 500 (l.03 2 i) 



present value, Co = ^ = / - N - i 

 1.03" (1.031) 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, 



a (i.op" i ) 



present value of series = -, - ^r-7 - ^ 

 (i.op i) (i.op n ) 



2. Assuming that the above series runs 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 



8 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 n i 



. 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. 



