FORMUL/E OF COMPOUND INTEREST 65 



and the erroneous use of these latter formulae leads to over- 

 valuation of assets. 



87. Relation Between Future Value of Temporary Annual 

 Rentals and Present, or Capital, Value of Same. In the 



formula for future value of temporary annual rentals, expressed 



as ^ (i.op n i) (7 9), the portion represents the capital 



o.op o.op 



value of a perpetual annual rental (XII), or the capital which 

 will produce an annual income of r. This formula might be 



expressed (i.op n ) : 



o.op o.op 



Substituting R for > 



o.op 



R = capital value of annual rental r. 



Then (i.op n ) = R X i.op" - R 



o.op o.op 



= R(i.op n - i). (Illb) 



This expression gives the sum of the compound interest, or 

 deferred income, earned by the capital R in n years, and is 

 obtained by computing the value of R at n years at p per cent, 

 and then subtracting the original capital. 



The numeral i substituted for R indicates that at any future 

 period the original capital remains intact. Since the sum of 

 the future values of an annual rental is thus shown to equal 

 the compound interest or income on its capitalized value, the 

 formula R (i.op n i) may be used to compute the total cost 

 not only of annual rentals, but of interest on invested capital 

 whenever the capital so invested remains intact at the end of 

 the period, as is the case with land. 



88. Conversion of Intermittent into Annual Rentals. To 

 convert an intermittent rental occurring every n years into its 

 equivalent annual rental, it is incorrect to divide the amount 

 of the intermittent rental by the factor n. The intermittent 

 rental is not received until n years from date, while the annual 

 rental is received in installments over the entire period, which 

 makes the average period of deferred payment less than half 

 as long. 



