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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