108 BULLETIN 136, U. 8. DEPARTMENT OF AGRICULTURE. 
bxample 18.—What is the bid on $100,000 highway 3% bonds maturing at the end 
of 3 years, interest payable semiannually, to net purchaser a nominal rate of 4% con- 
vertible half-yearly? 
Here n=3, g=.03, 7=.04, m=2, and formula (35) gives 
(OB 04) az 
Ce TALK Tae a 
a 
Hence the discownt on $100,000 is $2,800.72, and the corresponding bid is $97,199. 28. 
The progress of this bond loan is illustrated in the following schedule. 
= — .005 X 5.6014309= — .0280071545. 
SCHEDULE LY. 
Book val ¢ ‘ A lati Red ti 
ack | BARSHNSE | ceemmnan ss |) Seetennuat «| Pala | ea 
begrnget | Tero ajoubonde | eo a ae 
4 $97, 199. 28 $1, 943.99 | $1, 500.00 $443. 99 0. 00 
1 97, 643. 27 1, 952. 87 1, 500. 00 452. 87 0.00 
14 98, 096. 14 Is Giolly Ge 1, 500. 00 461. 92 0. 00 
2 98, 558. 06 COAG 1, 500. 00 471.16 0. 00 
24 | * 99,029. 22 1, 980. 58 1, 500. 00 480. 58 0. 00 
) 99, 509.80 | 1, 990. 20 | 1, 500. 00 490. 20 $100, 000. 00 
Totals} 590,035.77 | 11,800.72 | 9,000.00 | 2,800.72 100, 000. 00 
In this case the holder has an initial investment of $97,199.28, and 
at the end of the first half-year 2 per cent interest, or $1,943.99, is due. 
The dividend payment of $1,500.00, then made on the pomels, | is not 
sufficient to provide for this interest, and the difference of $443.99 is 
added to the principal and determines the book value at the beginning 
of the second half-year. This is called the accumulation or writing 
on of discount. By continuing this process for three years the 
entire discount of $2,800.72 is written on the imitial principal, and 
the book value, $100,000, is then redeemed. The totals of the several 
columns may be used to check the numerical work. 
Valuation of bonds redeemed in installments.—For the 
valuation of bonds which are not redeemed in one sum, but in a series 
of installments, first consider the simpler case where the dividend 
payments are pate and the rate of interest is the effective rate 2. 
Let 0,, C,,.... G,, denote the successive installments by which 
the bonds are to be redeemed; 
Wey es the respective number of years after 
which the successive installments 
become due; 
Gti RAs SUAS ne present values, a . effective re 
GPK he tl sent values, at the effective rate 
of interest 2, of 
C, due n, years hence 
1 1} ’ 
C, due n, years hence, 
C, due n, years hones: 
Se 
