FORMULA OF COMPOUND INTEREST. 119 



3. Summation of Rentals. 



a. Future Value. 



A rental R becomes due for the first time after m years, and 

 is repeated altogether n times at intervals of m years ; its 

 value after m X n years is : 



- _B(l-op""-l) 



A rental r is due at the end of each year, altogether n times ; 

 its value at the end of n years is : 



b. Present Value. 



A rental R becomes due for the first time after m years, and 

 is repeated n times after intervals of m years ; its present 



value is : 



r = R(l'op mn -l) , y } 



I-op mn (l'op m -l) 



A rental r is due at the end of each year, altogether n times ; 

 its present value is : 



r l--l 



~ 1-pp-x-op- 



A rental r is due at the end of each year, for ever ; its 

 present value is : 



O= . . . . (VII.) 



'op 



A rental R is due after n years, and again every n years, for 

 ever ; its present value is : 



A rental R is due after m years, and again every n years, for 

 ever ; its present value is : 



