Question

ssume that 3-month Treasury bills totaling $13 billion were sold in $10,000 denominations at a discount rate of 3.650%. In addition, the Treasury Department sold 6-month bills totaling $11 billion at a discount rate of 3.595%.

a. What is the discount amount for 3-month bills? (Do not round intermediate calculations. Round your final answer to the nearest cent.)

Discount amount for 3-month bills            $

b. What is the discount amount for 6-month bills? (Do not round intermediate calculations. Round your final answer to the nearest cent.)

Discount amount for 6-month bills            $

c. What is the effective rate for 3-month bills? (Do not round intermediate calculations. Round your final answer to the nearest hundredth percent.)

Effective rate for 3-month bills             %  

d. What is the effective rate for 6-month bills? (Do not round intermediate calculations. Round your final answer to the nearest hundredth percent.)

Effective rate for 6-month bills             %

Answer 1

Normally, T-bills are issued at a discount rate and redeemed at par value.

Discount Amount = Par value of T bill * discount rate

Discounted Price of T-bills = Par value - Discount Amount

Effective interest rate = Discount Amount/Discounted Price of T-bills

Information Provided

3-month T-bills

Total Amount of T-bills sold = $ 13,000,000,000

Par value of one T-bill = $ 10,000

No. T-bill sold = 1,300,000

Discount rate = 3.650%

6-month T-bills

Total Amount of T-bills sold = $ 11,000,000,000

Par value of one T-bill = $ 10,000

No. T-bill sold = 1,100,000

Discount rate = 3.595%

a) Discount Amount of 3-month T-bills

Discount Amount = Par value * Discount rate

= 10,000 * 0.0365

= $ 365

Total Amount of Discount = 365*1,300,000 = $ 474,500,000

b) Discount Amount of 6-month T-bills

Discount Amount = Par value * Discount rate

= 10,000 * 0.03595

= $ 359.5

Total Amount of Discount = 359.5*1,100,000 = $ 395,450,000

c) Effective rate for 3-month bills

Effective rate = Discount amount/Discounted Price

= 365/(10,000-365)

= 365/9,635

= 0.03788

= 3.79 %

c) Effective rate for 6-month bills

Effective rate = Discount amount/Discounted Price

= 359.5/(10,000-359.5)

= 359.5/9,640.5

= 0.03729

= 3.73 %

Hope this will help, please do comment if you need any further explanation. Your feedback would be appreciated.