# 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.

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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.

So. P=10000*(1-0.0174*(153/360))=9926.05

the cost of purchasing this bond is 9926.05