FORMULA OF COMPOUND INTEREST 6l 



determined for the date of the final payment, falling in the 

 year nt, the interval elapsing subsequent to this payment is 

 zero. When this payment falls at some previous date, a, the 

 total value at that date accumulates interest during the remain- 

 ing period. This period is equal to n a years. 

 The series forming the sum of the rentals is 



V r = / (l.O/>-) + / (l.O/"-) ' + / (l.<tf"~). 



By use of Formula Qi, substituting the ratio i.op n for q, and 

 the factor t for n, this becomes 



_ 



i.op n - 



By multiplying Formula V by i.op n ~ a (see Formula I), the 

 same result is obtained. 



85. Present, Expectation, or Capital Value of Temporary 

 Intermittent Rentals, Due First in a Years, and t Times at 

 Intervals of n Years Thereafter. The present value of the 



first payment, due in a years, is (II) . The period a may be 

 of any length and may exceed n. The present value of subse- 

 quent payments diminishes by the constant ratio , form- 

 ing the series 



r ' r ' 



I 



i.op a i.op a+n i.o/> a + 2n 

 To obtain the sum of present values (Q 2 ), 



g = 



i.op a 



i 



i.op n 



-U- 



i.op a \ i.op nt J 

 * i 



i.op n 



I.O/> 



