VALUES 9 



reinvested, the total investment will have increased by an amount 

 representing the interest on the total sum on hand at the begin- 

 ning of the period. A sum earning interest in this manner 

 increases at a compound or geometric rate. 



Should the annual interest earned be withdrawn annually, 

 neither the principal nor the interest earned would increase in 

 amount. Should this interest be saved but not reinvested, the 

 total value of principal and accumulated interest would increase 

 by the same amount annually. This is termed simple interest. 

 In neither of these cases is compound interest obtained. Com- 

 pound interest is paid by savings banks on deposits which remain 

 untouched for periods of six months or more. 



Since the earning of interest on money, without expenditure 

 or withdrawal of the earnings, is equivalent to depriving the 

 owner of this capital of all use of his property for the period 

 covered by the loan, the difference in value of the capital at 

 the beginning and end of the period measures the money value 

 of the period of waiting. When money is loaned for periods 

 exceeding one year, this difference in value must be computed 

 by compound interest. Any lesser sum would fall short of the 

 demonstrated earning power of money capital at a given rate 

 of interest. Since compound interest is thus required for money 

 loans it must be accepted also as the standard of time differences 

 in value for all other forms of income. 



By means of compound interest at a given rate the exact 

 ratio is obtained by which present values may be converted 

 into future values, or, by discount, future values may be re- 

 duced to their present equivalents. When both the present 

 and future values are known, a rate of compound interest may 

 be found which will equalize the difference in time and convert 

 the one value into the other. 



17. Sale Value. The sale value of property is indicated 

 by recent prices for similar property in the same locality. In 

 the absence of actual sales it is difficult to determine present 

 sale value. 



Sale values are not uniform for the same kind and quality of 

 goods, even in the same locality, unless there is a complete 



