HIGHWAY BONDS. 115 
ScHEDULE VII. 
(Schedule I adjusted to bonds of denomination $100.) 
| : Annuit Amortization | Amountof | 
Sipar Saniroslse . Suen Heels of premium pondsneited | 
; beginning of 9107 . at end of at end of at end of 
half-year. 270 half-year. half-year. half-year. 
s $100, 000 $2, 500. 00 $18, 200. 00 0. 00 | $15, 700 
1 84, 300 2, 107. 50 18, 107. 50 0. 00 16, 000 
13 68, 300 1, 707. 50 18, 107. 50 0. 00 16, 400 
2 51, 900 1, 297. 50 18, 197. 50 0. 00 16, 900 
25 30, 000 875. 00 18, 175. 00 0. 00 17, 300 
3 17, 700 442. 50 18, 142. 50 0. 00 17, 700 
Totals 397, 200 8, 950. 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 g=.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. 
Scuepute VIII—Showing the progress of an annuity bond issue of $100,000, denomi- 
nation $100, bearing 5 per cent interest, compounded senvannually, 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 
Near: 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. 
S $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 
ly 69, 130. 89 1, 382. 62 US NO. 50) 324. 88 16, 400 
2 52, 406. 01 1, 048. 12 18, 197. 50 249. 38 16, 900 
23 30, 256. 63 705. 13 18, 175. 00 169. 87 7 S00 
3 eee ie786: 76 85D. 7 118, 142550 86. 76 17, 700 
Totals | 361, 802. 07 | 7,236.05 | 108,930.00 | 1, 693. 95 100, 000 
