22 



BULLETIN 136, U. S. DEPARTMENT OF AGRICULTURE. 



interest, the term of the bond is thereby absolutely fixed. A simple 

 way to accomplish this result is to add to the nominal interest rate 

 which the bonds pay a percentage of the principal to be set aside in a 

 sinking fund to retire the bonds. There is produced thus a new nomi- 

 nal rate. Since both interest and principal are discharged by the 

 periodical payment of interest or dividends at the new nominal rate, 

 an issue of this character may be described as a special form of an- 

 nuity bond. 



Table 15 shows the resulting terms hi years of a bond issue for 

 $1,000,000 where from 1| to one-half per cent of the principal is set 

 aside semiannually in a sinking fund which draws 3 per cent com- 

 pounded semiannually. The original interest rate on the bonds is 

 assumed to be 3 per cent, payable semiannually, and the new in- 

 creased nominal rate varies then from 6 to 4 per cent. The last col- 

 umn shows the total cost to the borrower for the loan of $1,000,000 

 under this method. 



Table 15. — Necessary terms and total costs of a bond issue of SI, 000, 000 at 3 per cent, 

 payable semiannually, when retired by various arbitrary fractions of the principal set 

 aside and compounded semiannually. 



Applied 









semiannu- 

 ally to 

 sinking 

 fund to 



retire bond 

 issue. 



increased 

 interest 



Term of 



Total cost to 



rate on 



original 



3% bonds. 



bonds. 



borrower. 



Per cent, of 









loan. 



Per cent. 



Years. 



Dollars. 



1H 



6 



23J4 



1,410,000 



lVs 



5% 



25 



1, 437, 500 



1M 



&A 



2$y 2 



1,457,500 



m 



5M 



2&Vi 



1,496,250 



i 



5 



31 



1,550,000 



Vs 



4^ 



34 



1,615,000 



H 



4^ 



37 



1,665,000 



% 



4M 



413^ 



1, 763, 750 



X 



4 



47 



1,880,000 



% 



4 



50 



2, 000, 000 



The progress of the accumulation of the semiannual sinking fund 

 under the plan here outlined is shown for varying retirement rates in 

 Table 17. It is possible so to determine the rate of retirement that 

 the resulting term of the bonds is integral instead of fractional. The 

 increased nominal rates for 3 per cent bonds to retire in varying 

 integral terms is as follows : x 



Table 16. — Equivalent nominal rates for retiring 3 per cent bonds in varying terms. 



Per cent. Per cent. 



10 years 11. 649148 



20 years 6. 685420 



25 years 5. 711336 



30 years 5. 078686 



40 years 4. 309664 



50 years 3. 874114 



1 This rate per cent is determined by the formula: 



Rate per cent=3+200/S^7j 

 where n is the number of years S^rr, is determined from Table 32, Appendix D, at the rate 1|%. 



