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.
you can use formula d=((FV-P)/FV)*(360/n) to calculate the price of bond.
d is discount rate.
FV is face value.
P is price.
n is number of days to maturity.
the cost of purchasing this bond is 9926.05