CHAPTER V 

 FORMULAE OF COMPOUND INTEREST 



74. The Discount Factor. The mathematical relation be- 

 tween present and future values is expressed by formulae. By 

 substituting the desired rate of interest in the formula the ratio 

 is found by which the one value may be converted into the other. 

 This ratio may be termed the "discount factor." 



75. Rentals. The term "rental" is used to denote a 

 definite sum recurring as income at regular intervals. The 

 interval may be of any length, even one hundred years, provided 

 the payment is assumed to recur periodically. Since income 

 to one person means outlay to another, the amount of an expense 

 occurring at regular periods is obtained by treating it as a rental. 

 The sum of the future values of a series of payments consti- 

 tuting a rental must frequently be determined, as well as the 

 discounted or present value of this sum. 



The formulas needed in valuation are those which will deter- 

 mine : 



The future value of single sums. 



The present value of future sums. 



The future value of the sum of rentals. 



The present value of the sum of future rentals. 



The ratio between present and future values. 



76. Future Value or Cost of Single Sums. 



V = value of capital or sum. 

 VQ = value at beginning of period. 

 V n = value at end of period. 



Vi, Vz = value at end of years indicated by numeral. 

 n = period intervening before final reckoning. 

 p = rate of interest adopted. 



W.W^Xj J.J.J. IVslV/Ol, V/AJJ 



53 



= o.op, interest expressed decimally. 

 100 



