16 



BULLETIN" 136, U. S. DEPARTMENT OF AGRICULTURE. 



of the community are in, a way to become much confused. This is 

 particularly true since the officers in charge of such operations are 

 frequently changing. Sinking fund tax levies may be deferred 

 through carelessness or under pressure of other needs. The sinking 

 fund always requires careful attention, because it does not progress 

 automatically in most cases. 1 It has sometimes been entirely neg- 

 lected. The total cost of a bond issue retired by a sinking fund will 

 be greater in the end than the cost of the same bond issue made by 

 either the annuity method or by the serial method. 



Annuity bonds. — By the annuity method of issuing bonds both 

 the principal and interest are discharged by constant annual or semi- 

 annual payments. The amount of each payment or installment is 

 determined by the rate of interest and the term of the bond. It usu- 

 ally is necessary to subdivide the bond issue into individual bonds of 

 $100, $500, or$l,000 each. The resulting periodic payment of principal 

 and interest must vary slightly because of this adjustment. Tables 8 

 and 9 show, in detail, the schedule of principal and interest repayments 

 upon a loan of $100,000 for 20 years, retired by this plan at 4 and 5 

 per cent per annum, respectively. The necessary adjustment to the 

 nearest $100 bond is also shown. It will be seen that the amount of 

 principal retired is small at first and constantly increases while the 

 interest charge decreases. The sum of interest and principal re- 

 mains constant, and this is an advantage as the tax is then uniform. 



Table 8. 



-Repayment of a 4 per cent $100,000 loan, including both principal and interest, 

 by a uniform annual payment of $7,358,175 for 20 years. 2 



Adjusted to nearest cent. 



Adjusted to $100 bonds. 





Principal 





Principal 



Princi- 

 pal owing 

 at begin- 





Princi- 





Years. 



owing at 

 beginning 



Interest 

 for year. 



repaid at 

 end of 



Interest 

 for year. 



pal repaid 

 at end of 



Total. 





of year. 





year. 



year. 





year. 





1.... 



$100, 000. 00 



S4.000.00 



S3, 358. 18 



$100, 000 



$4,000 



$3, 400 



S7, 400 



2.... 



96,641.82 



3, 865. 67 



3,492.50 



96, 600 



3,864 



3,500 



7, 364 



3.... 



93,149.32 



3,725.97 



3,632.21 



93, 100 



3,724 



3, 600 



7,324 



4.... 



89, 517. 11 



3,580.68 



3,777.49 



89, 500 



3,580 



3,800 



7,380 



5.... 



85,739.62 



3, 429. 59 



3, 928. 59 



85, 700 



3, 428 



3,900 



7, 328 



6.... 



81,811.03 



3,272.44 



4,085.73 



81,800 



3,272 



4,100 



7,372 



7.... 



77, 725. 30 



3, 109. 01 



4,249.17 



77, 700 



3,108 



4,200 



7,308 



8 



73,476.13 



2,939.05 



4,419.12 



73,500 



2, '11(1 



4,400 



7,340 



9.... 



69, 057. 01 



2, 762. 28 



4,595.90 



69, 100 



2,764 



4,600 



7,364 



10.... 



64,461.11 



2,578.44 



4,779.73 



64,500 



2,580 



4,800 



7, 380 



11.... 



59.681.3S 



2,387.26 



4,970.92 



59, 700 



2, 3SS 



5.000 



7,388 



12.... 



54,710.46 



2, 188. 42 



5,169.75 



54,700 



2. 1SS 



5,200 



7,388 



13 



49,540.71 



1,981.63 



5, 376. 55 



49, 500 



1,980 



5,400 



7,380 



14.... 



44,164.16 



1,766.57 



5,591.60 



44,100 



1,764 



5,600 



7,364 



15.... 



38, 572. 56 



1,542.90 



5, S15. 28 



38, 500 



1,540 



5,800 



7.340 



16.... 



32.757.2S 



1,310.29 



6,047.88 



32, 700 



1,308 



6,000 



7.308 



17.... 



26,709.40 



1.068.38 



6,289.80 



26, 700 



1,068 



6,300 



7,368 



18.... 



20; 419. 60 



816.78 



6.541.39 



20, 400 



mi; 



6, 500 



7.316 



19.... 



13,878.21 



555. 13 



6.S03.05 



13,900 



556 



6, 800 



7,356 



20. . . . 

 Totals 



7,075.16 



283.01 



7,075.16 



7.100 



284 



7.100 



7,384 





47, 163. 50 



100, 000. 00 





47, 152 



100, 000 



147,152 







1 In some States there are restrictions on the nature of county investments for sinking fund purposes. 



2 An additional table showing the annual payments necessary to discharge a loan of $1, with interest 

 for varying terms and rates, is given in Table 36 on pages 126 and 127. 



