CHAPTER 5
3.
Find the prices of the following Treasury bills per dollar of par:
(a) 40 days, discount rate of 6 percent
(b) 90 days, discount rate of 12 percent
(c) 80 days, discount rate of 8 percent
(d) 92 days, discount rate of 7 percent.
 Discount rate(Time) 
Price  par1 

360


a. P  1001 
0.06(40) 
  99.33
360 
b. P  1001 
0.12(90) 
  97.00
360 
c. P  1001 
0.08(80) 
  98.22
360 
d. P  1001 
0.07(92) 
  98.21
360 




4.
In problem 3, find the add-on interest rates, bond equivalent
yields, semiannual, and annual yields to maturity.
Add-on rate =
d
d(t )
1
360
Bond equivalent yield = r =
par
Semiannual YTM = i = 2 
 P 
par
Annual YTM = Y =  
 P 
( 365 / 2 t )
2
( 365 / t )
1
365
a
360
a. a 
0.06
 0.0604
(0.06)40
1
360
r
365
(0.0604)  0.0612
360
 100 
i  2
 99.33 
 100 
y
 99.33 
365 / 2 ( 40)
 2  0.0620
365 / 40
 1  0.0629
b. a 
0.12
 0.1237
(0.12)90
1
360
r
365
(0.1237)  0.1254
360
 100 
i  2
 97.00 
 100 
y
 97.00 
365 / 2 ( 90)
 2  0.1274
365/ 90
 1  0.1315
c. a 
0.08
 0.0815
(0.08)80
1
360
r
365
(0.0814)  0.0826
360
 100 
i  2
 98.22 
 100 
y
 98.22 
365 / 2 ( 80)
 2  0.0835
365 / 80
 1  0.0853
d. a 
0.07
 0.0713
(0.07)92
1
360
r
365
(0.0713)  0.0723
360
 100 
i  2
 98.21
 100 
y
 98.21
5.
365 / 2 ( 92)
 2  0.0729
365 / 92
 1  0.0742
Determine Treasury bill discount rates, assuming the following
information. Assume $1 par values:
(a) P = 0.96, t = 91 days
(b) P = 0.94, t = 91 days
(c) P 0.98, t = 91 days
(d) P = 0.98, t = 90 days.
d
(360) 
P 
1 

t  par 
a. d 
(360) 
96 
1 
  0.1582
91  100 
b. d 
(360) 
94 
1 
  0.2374
91  100 
c. d 
(360) 
98 
1 
  0.0791
91  100 
d. d 
(360) 
98 
1 
  0.0800
90  100 
6.
Assume a discount rate of 6 percent. Compute the add-on
interest rate, the bond equivalent yield, the semiannual and
annual yield to maturity for 30, 60, 90, 180 days. Graph these
results.
a. 30 days: P  1001 

0.06(30) 
  99.50
360 
a
0.06
 0.0603
0.06(30)
1
360
r
365
(0.0603)  0.0611
360
 100 
i  2
 99.50 
 100 
y
 99.50 
365 / 2 ( 30)
 2  0.0619
365 / 30
 1  0.0629
b. 60 days: P  1001 

0.06(60) 
  99.00
360 
a
0.06
 0.0606
0.06(60)
1
360
r
365
(0.0606)  0.0614
360
 100 
i  2
 99.00 
 100 
y
 99.00 
365 / 2 ( 60)
 2  0.0621
365 / 60
 1  0.0630
c. 90 days: P  1001 

0.06(90) 
  98.50
360 
a
0.06
 0.0609
0.06(90)
1
360
r
365
(0.0609)  0.0618
360
 100 
i  2
 98.50 
 100 
y
 98.50 
365 / 2 ( 90)
 2  0.0622
365 / 90
 1  0.0632
d. 180 days: P  1001 

a
0.06
 0.0619
0.06(180)
1
360
r
365
(0.0619)  0.0627
360
 100 
i  2
 97.00 
 100 
y
 97.00 
7.
0.06(180) 
  97.00
360 
365 / 2 (180)
 2  0.0627
365 / 180
 1  0.0637
Suppose that you are considering investing in two 91-day
money market instruments—Treasury bills with a discount rate
of 5 percent or commercial paper with a bond equivalent yield
of 5.20 percent. Which investment is better?
t = 91
d = 0.05
a
0.05
 0.0506
0.05(91)
1
360
r
365
(0.0506)  0.0513
360
T bills: r = 5.13%
Commercial Paper: r = 5.20%
Commercial Paper is a better investment.
8.
Suppose that a 90-day Treasury bill has a bond equivalent yield
of 2.75 percent. Compute the discount rate and the add-on
interest rate.
P
d
par
100

 99.326485
rt
1  (0.0275)(90 / 365)
1
365
360 
P  360
1  0.99326485  2.69%
1


t  par  90
1
 par   360  
 360
a
 1 

 1
 2.71%

 P
  t   0.99326485  90
9.
Suppose a Treasury bill with a maturity of 90 days and par
value of $100 has a discount rate of 5.25%. Determine the addon rate.
a
10.
d
0.0525

 5.3198%  5.32%
dt
1  0.0525(90 / 360)
1
360
Suppose a Treasury bill with a maturity of 100 days and par
value of $100 has a price of $98.89. Determine its discount
rate.
P   360 
 360  
d
 1 
1  0.9889

 t   par   100 
 3.9960%  4.00%
11.
Suppose a Treasury bill with a maturity of 90 days has an
annualized semiannually compounded yield to maturity of
5.69%. Determine the discount rate.
P
par
i

1  
 2
2 t / 365

100
100

 98.626
180 / 365
(1.02845)
(1.02845) 0.493151
P 
 360  
d
 1 
  5.4956%  6.00%
 t   par 