FORMULA OF COMPOUND INTEREST 59 



The same result may be obtained by discounting the final 

 future value of the sum of these rentals to the present (II). 



This future value V r = 



O.Qp 



Hence r(i.op n i) i _ r (i.oft* i) 



o.op i. op* o.op X i. op* 



Since capital value is the net value of income discounted to 

 the present, the application of this formula is evident. It may 

 be used to discount either annual income or annual expenses. 

 Should the two occur simultaneously, only the net annual 

 profit or loss is thus discounted. 



82. Future Value of Temporary Intermittent Rentals Due 

 First at n Years, and t Times at Intervals of n Years There- 

 after. A rental which occurs at intervals greater than one 

 year is termed intermittent, although if the interval is regular 

 it does not differ in character but only in degree from annual 

 or monthly rentals. 



Let n = period between rentals. 



/ = number of payments expected. 

 nt = total period covered by the investment. 

 / = intermittent rentals due at intervals of years. 

 V r = total value of intermittent rentals at end of period. 



The future value of the sum of these rentals, if computed in 

 the year of payment of the final rental, is 

 Final payment = /, 



Payment, n years preceding = / (i.op*), 

 Payment, 2 n years preceding = / (i.o/^ 2 "), 

 First payment = / (i .o^*-^ "). 



By use of Formula Qi, the sum of these terms is found by 

 substituting the ratio i.op n for q and the factor t for n. 

 The formula then reads: 



>. (V) 



Either income or expenses which terminate at a definite 

 date are far more apt to occur annually than at longer intervals 



