114 BULLETIN 136, U. S. DEPARTMENT OP AGRICULTURE. 



Schedule VI. 



Year. 



Book value or 



principal at 



beginning of 



half-year. 



Semiannual 

 interest of 



Semiannual 



dividend 



of 2% on 



bonds. 



Amortization 



of premium 



at end of 



half-year. 



Redemption 

 payment 

 at end of 

 half-year. 



1 

 1 



1J 



2 



2i 



3 3 

 Totals 



§305, 753. 73 

 304, 340. 04 

 202, 905. 14 

 201, 948. 72 

 100, 977. 95 

 100, 492. 62 



$4, 586. 31 

 4, 565. 10 

 3, 043. 58 

 3, 029. 23 

 1, 514. 67 

 1, 507. 38 



$6, 000. 00 

 6, 000. 00 

 4, 000. 00 

 4, 000. 00 

 2, 000. 00 

 2, 000. 00 



$1, 413. 69 

 1, 434. 90 

 956. 42 

 970. 77 

 485. 33 

 492. 62 



0.00 

 $100, 000. 00 



0.00 

 100, 000. 00 



0.00 

 100, 000. 00 



1, 216, 418. 20 



18, 246. 27 



24, 000. 00 



5, 753. 73 



300, 000. 00 



Annuity bonds. — On pages 101 to 104 the operation of a loan 

 where both principal and interest are discharged by equal install- 

 ments is fully described. It is evident that bonds may be issued 

 on this basis and retired in accordance with the principal repayments 

 contained in the annuity installments. Since these principal repay- 

 ments are not exact multiples of the amounts or denominations in 

 which bonds are usually issued, it is necessary to adjust the exact 

 schedule so as to meet this requirement. The adjusted schedule 

 gives an issue in which the bonds are retired year by year in increasing 

 amounts. Examples of exact and adjusted schedules appear in the 

 body of this bulletin on pages 16 and 17. 



To finance a loan of L by an issue of annuity bonds bearing 

 interest or dividends at rate g per annum. — The annual install- 

 ment which will retire the bonds in n years and at the same time 

 pay interest at the rate of g per cent on outstanding bonds is 



Lift',,] 



at rate g. 



(51) 



If the bonds are to bear interest of g per cent per annum, pay- 

 able in p installments of g/p per cent during the year, then 



LI ft; 



at rate g/p 



(52) 



is the periodical payment or annuity installment which wall take 

 care of interest on the bonds and retire them in n years. 



Example 24. — Adjust Schedule I, page 102, to finance the same loan by an annuity 

 bond issue of $100,000, denomination $100, bearing 5% interest, compounded semi- 

 annually, and retired in three years by six equal (nearly) semiannual annuity install- 

 ments. 



Referring to Schedule I on page 102, the adjustments in the last column to even 

 multiples of $100 are easily made; a check on this work is that the adjusted column 

 must foot up to $100,000. When the column of bond redemptions is decided upon, 

 the other columns in the schedule are readily derived. 



