U. S. Treasury bill yield calculations
[Pages:2]U. S. Treasury bill yield calculations
A problem set prepared by Pamela Peterson Drake, Florida Atlantic University
Formulas
Discount-basis yield =
face value - purchase price
360
face value
number of days to maturity
I nvestment yield =
face value - purchase price
365
purchase price
number
of
days
to
maturity
1. For each of the following Treasury Bills, calculate the discount basis yield and the investment yield:
T- Bi l l A
Mat urit y Price per $100
28-day
99.7667
Discount basis yield
I nvestment yield
B
91-day
C
182-day
99.2480 98.3190
D
14-day
E
91-day
F
182-day
99.8769 99.2214 98.4631
2. Suppose the investment yield on a 182-day T-bill is 4% . What is its discount- basis yield?
U. S. Treasury bill yield calculations
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Solut ion s
1.
T- Bi l l A B C D E F
Maturity 28-day 91-day 182-day 14-day 91-day 182-day
Price per $100 99.7667 99.2480 98.3190 99.8769 99.2214 98.4631
Discount basis yield
3.000% 2.975% 3.325% 3.165% 3.080% 3.040%
I nvestment yield
3.04 8 % 3.039% 3.429% 3.213% 3.147% 3.130%
Example: T-Bill A
Discount-basis yield =
$100 - 99.7667 $100
360 28
=
( 0.002333 )
(12.85714
)
=
2.99957%
I nvestment yield =
$100 - 99.7667 $99.7667
365 28
=
(0.00233846)
(13.035714)
=
3.04835%
2. First, solve for the purchase price of the T-bill, given the investment rate and the days to
m at ur it y:
$100 P
-
P 365 182
=
$100 P
-
P
(2.005495)
=
4%
Solve for P in
$100 P
-
P
=
0.04 2.005495
using Algebra:
$100 -
P =
0.04 2.005495
P
$100 =
0.04 2.005495
P
+
P =
1+
0.04 2.005495
P
$100 = 1.019945 P
P = $98.044483
Second, solve for the discount-basis yield:
Discount-basis yield =
$100
- 98.044483
$100
360 182
=
(0.019555 ) (1.978022 )
=
3.86802%
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