HIGHWAY BONDS. 



115 



Schedule VII. 

 (Schedule I adjusted to bonds of denomination $100.) 



Year. 



Book value or 



principal at 



beginning of 



half-year. 



Semiannual 



interest of 



2£%- 



Annuity 



installments 

 at end of 

 half-year. 



Amortization 



of premium 



at end of 



half-year. 



Amount of 



bonds retired 



at end of 



half-year. 



i 



1 



2 



9i 



3 



Totals 



$100, 000 • 

 84, 300 

 68, 300 

 51, 900 

 35, 000 

 17, 700 



$2, 500. 00 



2, 107. 50 



1, 707. 50 



1, 297. 50 



875. 00 



442. 50 



$18, 200. 00 

 18, 107. 50 

 18, 107. 50 

 18, 197. 50 

 18, 175. 00 

 18, 142. 50 



0.00 

 0.00 

 0.00 

 0.00 

 0.00 

 0.00 



$15, 700 

 16, 000 

 16, 400 



16, 900 



17, 300 

 17, 700 



357, 200 



8, 930. 00 



108, 930. 00 



0.00 



100, 000 



Valuation of annuity bonds. — In order to value an issue of 

 this character, so as to yield the purchaser a net income at a rate of 

 interest different from the rate of dividend on the bonds, it will ordi- 

 narily be necessary to value separately the several parts of the total 

 issue in accordance with the respective dates on which they are re- 

 tired. This calculation may frequently be shortened by employing 

 formula (36). Bond tables may also be consulted to advantage. 

 The following example and schedule respectively illustrate the cal- 

 culation of the bid and progress of the loan. 



Example 25. — Determine the bid on the entire issue of annuity bonds in Example 

 24 so as to yield the investor a net income of 4%, compounded semiannually. 



Applying formula (35) successively to the several bond issues in the order in which 

 they are retired with ^=.05 and J=.04, the following premiums are found: 



$76. 96 



155. 32 



236. 48 



321. 75 



407. 71 



495. 73 



$1, 693. 95 

 Accordingly, the bid on the entire issue is $101,693.95. The schedule illustrating 

 the progress of this bond issue follows. It is constructed in the same manner as pre- 

 ceding bond schedules and needs no additional explanation. 



Schedule VIII. — Showing the progress of an annuity bond issue of $100,000, denomi- 

 nation $100, bearing 5 per cent interest, compounded semiannually, and retired in three 

 years by six equal {nearly) semiannual annuity installments. Bought to yield the 

 investor 4 per cent, compounded semiannually. 





Book value or 





Annuity 



Amortization 



Amount of 





principal at 



Semiannual 



installments 



of premium 



bonds retired 





beginning of 



interest of 2%. 



at end of 



at end of 



at end of 





half-year. 





half-year. 



half-year. 



half-year. 



X 



$101, 693. 95 



$2, 033. 88 



$18, 200. 00 



$466. 12 



$15, 700 



1 



85, 527. 83 



1, 710. 56 



18, 107. 50 



396. 94 



16, 000 



14 



69, 130. 89 



1, 382. 62 



18, 107. 50 



324. 88 



16,400 



2 



52, 406. 01 



1, 048. 12 



18, 197. 50 



249. 38 



16, 900 



n 



35, 256. 63 



705. 13 



18, 175. 00 



169. 87 



17, £00 



3 

 Totals 



17, 786. 76 



355. 74 



18, 142. 50 



86.76 



17, 700 



361, 802. 07 



7, 236. 05 



108, 930. 00 



1, 693. 95 



100, 000 



