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



Table 11. — Schedule of interest and principal to retire a serial loan of $100,000 at 5 per 

 cent, with annual principal repayments of $5,000. 



Years. 



Principal 

 outstand- 

 ing at 

 beginning 

 of year. 



Interest 

 for year. 



Principal 

 repaid at 



end of 



year. 



Total. 



Years. 



Principal 

 outstand- 

 ing at 

 beginning 

 of year. 



Interest 

 for year. 



Principal 



repaid at 



end of 



year. 



Total. 



1 



$100,000 



$5,000 



$5,000 



$10,000 



12 



$45,000 



$2,250 



$5,000 



$7,250 



2 



95,000 



4,750 



5,000 



9,750 



13 



40,000 



2,000 



5,000 



7,000 



3 



90, 000 



4,500 



5,000 



9,500 i 



14 



35,000 



1,750 



5,000 



6,750 



4 



85,000 



4,250 



5,000 



9,250 ; 



15 



30,000 



1,500 



5,000 



6,500 



5 



SO, 000 



4,000 



5,000 



9,000 



16 



25,000 



1,250 



5,000 



6, 250 



6 



75,000 



3,750 



5,000 



8,750 



17 



20,000 



1,000 



5,000 



6,000 



7 



70, 000 



3,500 



5,000 



S.500 



18- 



15,000 



750 



5,000 



5,750 



8 



65,000 



3,250 



5,000 



8,250 



19 



10,000 



500 



5,000 



5, 500 



9 



60, 000 



3,000 



5,000 



8,000 



20 



5,000 



250 



5,000 



5,250 



10 



55,000 



2,750 



5,000 



7,750 





















11 



50,000 



2,500 



5,000 



7,500 



Totals. 





52,500 



100,0110 



152, 500 





Comparison of serial, annuity, and sinking-fund bonds.— 



It will be noticed that the total expense to the community under the 

 serial plan is somewhat less than under the annuity plan. The 

 expense by either method is, however, considerably less than the 

 expense under the sinking-fund plan. For the purpose of comparison 

 the total expense to the community under each plan is assembled 

 under Table 12. 



Tables 8 to 11, inclusive, are computed with interest payable 

 annually. Bonds with interest payable semiannually sell better. 

 Similar tables or schedules for the annuity and serial plans of bond 

 issues to conform to semiannual interest payments can be easily 

 prepared. Schedules can also be prepared to show the progress of a 

 bond loan when the bonds are bought at a premium or discount. 1 



Table 12. — Total cost of a loan of $100,000 for 20 years, interest compounded annually . 



Annual 

 interest 



on 

 bonds. 



Sinking fund compounded 

 annually at— 



Annuity. 



Serial. 



3 per cent. 



3| per 

 cent. 



4 per cent. 



4 



4* 



5 



5i 



6 



$154,431 

 104,431 

 174,431 

 184,431 

 194,431 



$150,722 

 160,722 

 170,722 

 180, 722 

 190,722 



$147,163 

 157, 163 

 167, 163 

 177,163 

 187, 163 



$147, 163 

 153,752 

 160,485 

 167,359 

 174,369 



$142,000 

 147,250 

 152,500 

 157,750 

 163.000 



In a bond issue by any given plan the amount, the interest, 

 and the term may be fixed at will, but when this is done the annual 

 repayments of principal and interest are theoretically determined. 

 Thus, by the annuity method, if $100,000 is to be issued at 5 per cent 

 annually and retired in 20 years, the annual amount of interest 

 and principal is at once determined to be approximately $8,000. 



1 Cf. Appendix D, pages 91 to 115, for details of such schedules. 



