Calculate the price for a T-bill with a face value of $10,000, 153 days to maturity, and a discount yield of 1.74 percent.

T-bills are sold at a discount to the face value and the
person buying the T-bill makes a profit equal to the difference between the face value
and the market price.

The discount yield of a T-bill is the
percentage profit that a person buying the T-bill at the present market price would be
able to make at expiration.

In the problem given, the time
to expiry is 153 days. As the face value of the T-bill is $10,000, an investor gets
$10,000 after 153 days. For these problems the year is usually taken to have 360
days.

So the annual discount yield of the T-bill is given
by [(10000 – Price) / 10000]*(360 / 153)

This is given to
us as 1.74% or 0.0174.

So [(10000 – Price) / 10000]*(360 /
153) = 0.0174

=> [(10000 – Price) / 10000] = 0.0174*
(153 / 360)

=> (10000 – Price) = .0174* (153 / 360)*
10000

=> (10000 – Price) =
73.95

=> Price = 10000-
73.95

=> Price =
9926.05

Therefore a T-bill of face value
$10,000 bought at $9926.05, gives a discount yield of 1.74% in 153
days.