FORMULAE OF COMPOUND INTEREST 55 



The arithmetical equivalent of l ^ may be expressed as a 



decimal. 



Discount formulae are used in valuation of assets. The 

 discounting of future "profits" or net income is identical with 

 the determination of capital value. There can be no value in 

 excess of this discounted net income ( 62). 



To obtain this net present value, future costs may be first 

 discounted and then subtracted from discounted gross income. 

 Or this subtraction may be made at any future period and the 

 net income discounted. If the values are properly computed 

 to the same year, before striking the balance, the discounted 

 results are identical. For instance, an expense c occurs in the 

 year d, which lies between the years o and n. 



The present value or equivalent of c will be 



i. op 



The future equivalent of c at the end of the year n will be 

 c X i.op n ~ d , since n d is the period over which interest on c 

 would accumulate. 



The present equivalent of c X i.op n ~ d will be 

 c X i.op n - d 

 i.op n 



Hence, to determine the net present value of future income, 

 future expenses may be computed forward to the year in which 

 the income is received, and subtracted from this income, and the 

 resultant net income discounted to the present. This accom- 

 plishes the same purpose as discounting each item of expense 

 to the present before subtracting it from gross income. The 

 choice of these methods is merely a matter of convenience. 



78. Use of Logarithms and Tables. The arithmetical 

 equivalents of these formulae are calculated by the use of loga- 

 rithms. The numeral representing the desired rate of interest 

 is substituted for p, and the number of years in the period for 

 n. For 4 per cent and 50 years, i.op n becomes z.04 50 . The 

 logarithm of i .04 is multiplied by 50. The result is the logarithm 

 of z.04 50 , from which the ratio is obtained. In the case cited, 

 the ratio is 7.1067, which indicates that $1.00 will increase in 



