APPENDIX D. 



THEORY OF INTEREST APPLIED TO HIGHWAY-BOND CALCULATIONS, 



WITH SINKING FUND, ANNUITY, AND INTEREST TABLES FOR 



60 INTERVALS AND 14 RATES OF INTEREST. 



TABLE OP CONTENTS. 



Page. 



Introduction 92 



Definitions 92 



Mathematical rates 93 



Commercial rate 93 



Relation between effective and nominal rates 



of interest 93 



Amount of 1 in n years at compound interest. 94 



The discount factor 95 



Annuities-certain 95 



Amount of an immediate annuity-certain ... 95 



Sinking fund which will amount to 1 97 



Present value of an immediate annuity- 

 certain 99 



Fundamental relations between the present 



value and the amount of an annuity 100 



The annuity which 1 will purchase 101 



Installment annuity loan 102 



C eneralization of the annuity loan 103 



Relation between annuity which 1 will pur- 

 chase and sinking fund which will amount 



to 1 - 104 



Application to bond calculations 104 



Dividends payable and interest convertible 



semiannually 107 



Valuation of bonds redeemed in installments. 108 

 Installment bonds when total sum to be re- 

 deemed is 1 109 



Page. 

 Serial bonds 110 



Extension of formulas to case when dividends 

 are payable and interest is convertible m 



times per annum 110 



General formula for valuation of bonds Ill 



Extension of term of tables 112 



Valuation of serial bonds bearing semiannual 



dividends 113 



Annuity bonds 114 



To finance a loan of L by an issue of annuity 

 bonds bearing interest or dividends at rate 



g per annum 114 



Valuation of annuity bonds 115 



Table 31. Accumulation of lat end of m years. 110 

 Table 32. Accumulation of annuity of 1 per 



annum at end of n years 118 



Table 33. Annual sinking fund which will 



accumulate to 1 at end of n years 120 



Table 34. Present value of 1 due in n years . . 122 

 Table 35. Present value of annuity of 1 for n 



years 124 



Table_36. Annuity for n years which 1 will buy 

 or annuity needed to discharge debt of 1 in 



n years with interest 126 



Table 37. Bid on bond for S100 to realize a 

 given net income, interest payable semi- 

 annuallv 128 



91 



