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 in years of a bond issue for — 
$1,000,000 where from 14 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.—WNecessary terms and total costs of a bond issue of $1,000,000 at 3 per cent, 
payable semiannually, when retired by various arbitrary fractions of the principal set 
aside and compounded senuannually. 
| 
Applied 
d New 
Seas increased 
siiving interest Term of | Total cost to 
aandtto rate on bonds. borrower. 
original 
retire bond | a 
eel 3% bonds. 
Per cent. of 
loan. Per cent. Years. Dollars. 
1% 6 231%, 1, 410, 000 
13% 53 25 1, 437, 500 
14% 516 2614 1, 457, 500 
1% 514 2814 1, 496, 250 
5 31 1, 550, 000 
% 434 34 1, 615, 000 
34 41% 37 1, 665, 000 
5% 44 4114 1, 763, 750 
% 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:! 
TaBLE 16.—LEquivalent nominal rates for retiring 3 per cent bonds in varying terms. 
Per cent. Per cent. 
MOBO Ree soe tte the ce er! 11649148. | SOs yearst ss eee 5. 078686 
ZORCAT Sepia ttys Aig OR Soot 6. 685420 | 40 years... <2s..2.-¢ ob ES eee 4. 309664 
AS) Et A ee 0. 714336, | 50" years: 228 2 eer ae sees 3. 874114 
1 This rate per cent is determined by the formula: 
Rate per cent=3+-200/S5, 
where 7 is the number of years S5 is determined from Table 32, Appendix D, at the rate 14%. 
