APPENDIX D. 



THEORY OF INTEREST APPLIED TO BOND CALCULATIONS. 



Introduction. — This appendix presents briefly the application of 

 the theory of compound interest to highway bonds. There are six 

 important quantities in terms of which the solution of most problems 

 can be expressed. If i is the rate of interest and n the term of years, 

 these quantities are: 



The accumulation of 1 at the end of n years, r n ; 



The accumulation of an annuity of 1 per annum at the end of n 

 years, s^; 



The annual sinking fund which will accumulate to 1 at the end of 

 n years, l/«s,; 



The present value of 1 due in n years, v n ; 



The present value of an annuity of 1 per annum for n years, a^; 

 and 



The annuity for n years which 1 will purchase, or the annuity 

 necessary to discharge a debt of 1 in n years with interest, 1/a^. 



The first three are accumulative functions and the last three are 

 discount or present value functions. 



The mathematical formulas for these six quantities are: 



(1 + *)**— 1 1 i 



i «ji (1 + ^-1 



The values of most of these functions are given more or less com- 

 pletely in published tables of interest. 1 



Definitions. — Interest may be defined as the consideration for the 

 use of capital. The capital is called the principal. 



The rate at which a given principal is earning interest requires 

 the adoption of some interval as the unit of time, and this is usually 

 the year. 



It is clear that interest when received may be added to the principal 

 and so in turn earn interest. This process, called compounding, takes 

 place at the end of stated intervals, as every three months, six months, 

 or year. 



J At the end of this appendix, pages 116 to 127, are short tables to seven places for 60 intervals and 

 14 interest rates. 



92 



