HIGHWAY BONDS. 



15 



at 3, 3^, and 4 per cent compounded semiannually for varying 

 periods from 1 to 30 years. 



Table 6. — Annual payments which, with interest at 3, 3\, and 4 per cent, compounded 

 semianually, will amount to §1,000 at the end of a term of years. 1 





Annual payments. 





Annual payments. 



Years. 









Years. 























3 per cent. 



3J per cent. 



4 per cent. 





3 per cent. 



3J per cent. 



4 per cent. 



1 



SI, 000. 0000 



81,000.0000 



SI, 000. 0000 



16 



S49. 5229 



S47. 5689 



845. 6734 



2 



492. 5562 



491. 3266 



490. 1000 



17 



45. 8652 



43. 9283 



42. 0537 



3 



323. 4583 



321.8368 



320. 2221 



18 



42. 6221 



40. 7032 



38. 8501 



4 



238. 9468 



237. 1428 



235. 3498 



19 



39. 7280 



37. S279 



35. 9976 



•5 



188.2699 



186. 3672 



184. 4796 



20 



37. 1306 



35. 2499 



33. 4426 



6 



154. 5102 



152. 5508 



150. 6104 



21 



34. 7875 



32. 9267 



31. 1429 



7 



130. 4175 



128. 4252 



126. 4560 



22 



32. 6639 



30. 8236 



29. 0636 



8 



112. 3666 



110. 3564 



108. 3733 



23 



30. 7313 



28.9116 



27. 1759 



9 



98. 3436 



96. 3254 



94. 3382 



24 



28. 9656 



27.1670 



25. 4557 



10 



87. 1402 



85.1208 



83. 1366 



25 



27. 3469 



25. 5696 



23. 8829 



11 



77. 9872 



75.9717 



73. 9954 



26 



25. 8582 



24. 1024 



22. 4404 



12 



70. 3721 



68. 3643 



66. 3996 



27 



24. 4850 



22. 7508 



21. 1136 



13 



63. 9399 



61. 9427 



59. 9924 



28 



23.2149 



21. 5024 



19. 8901 



14 



58. 4372 



56. 4527 



54. 5191 



29 



22. 0373 



20. 3465 



18. 7591 



15 



53. 6780 



51. 7080 



49. 7928 



30 



20. 9428 



19. 2739 



17. 7113 



1 In Appendix D, page 98, Example 9 shows the method of calculating this table. 



Table 7 illustrates how an annual sinking fund of $32,345.83 

 accumulates for three years to $100,000. 



Table 7.- — Accumulations of an annual payment of §32,345.83 with interest at 3 per cent 



compounded semiannually. 



Number 



of 

 6-month 

 intervals. 



Principal at 



beginning of 



6-month 



intervals. 



Interest 



during 



6-month 



intervals. 



Annual pay- 

 ment at end 

 of 6-month 

 intervals. 



Total 

 amount at 



end of 

 6-month 

 intervals. 



1 

 2 

 3 

 4 

 5 

 6 



SO. 00 

 0.00 

 32,345.83 

 32,831.02 

 65, 669. 32 

 66, 654. 36 



SO. 00 

 0.00 

 485. 19 

 492. 47 

 985. 04 

 999. 81 



SO. 00 

 32,345.83 



0.00 

 32,345.83 



0.00 

 32,345.83 



SO. 00 

 32,345.83 

 32, 831. 02 

 65,669.32 

 66, 654. 36 

 100, 000. 00 



To obtain the necessary annual payments to produce any multiple 

 of $1 it is necessary merely to multiply the tabular value in Table 6 

 by the corresponding multiple ; thus, an annual sinking fund payment 

 to retire $100,000 in 15 years at 3f per cent would be $5,170.80. 

 Table 33, pages 120 and 121, gives the yearly or periodic payments 

 necessary to accumulate $1 in a given number of years or periods 

 at varying rates of interest. 



There are objections to the sinking-fund method of retiring high- 

 way bonds. It may not be possible to obtain continuously the requi- 

 site rate of interest on the sinking fund to discharge the debt at 

 maturity. The existence of the sinking fund is a constant temptation 

 to municipal officers to use it for purposes other than the purpose 

 originally intended. If a county, for example, issues bonds for a 

 second object, it is easy to argue that the sinking fund already accu- 

 mulated may be used to purchase the new securities, and the finances 



