Question

6. (1) A 13 weeks T-bill with a face value of $100,000 was sold at an annual interest rate of 3% on Monday, August 31. If you purchase it on August 31, how much was the purchase price?

2. If you hold the T-bill until maturity (November 30,2020), how much will you receive from U.S. Treasury department on maturity date? How much is your annual effective interest rate?

3. If the annual interest rate drops to 2% 4 weeks later (on September 28, 2020), how much can you sell T-bill on that day? How much is the annual effective interest rate you earned from holding the T-bill for 4 weeks? Will you be better off to sell the T-bill on that day or hold it until maturity? Why?

Answer 1

6. (1) A 13 weeks T-bill with a face value of $100,000 was sold at an annual interest rate of 3% on Monday, August 31. If you purchase it on August 31, how much was the purchase price?

Ans: T-Bills are always issued at discount and redeemed at Par

Purchase Price = Face Value / (1 + Interest * 13 weeks/52 weeks)

Purchase Price = 100000 / (1 + 3%*13 /52 )

Purchase Price = 100000 / 1.0075

Purchase Price = $99255.58

2. If you hold the T-bill until maturity (November 30,2020), how much will you receive from U.S. Treasury department on maturity date? How much is your annual effective interest rate?

If you hold till maturity we get face value on maturity Date i.e., $100000

Annual Effective Interest Rate = (Face Value ) / Purchase price]^(52 / 13)

Annual Effective Interest Rate = (100000 ) / 99255.58]^4 - 1

Annual Effective Interest Rate = 1.0075^4 - 1

Annual Effective Interest Rate = 3.034%
3. If the annual interest rate drops to 2% 4 weeks later (on September 28, 2020), how much can you sell T-bill on that day? How much is the annual effective interest rate you earned from holding the T-bill for 4 weeks? Will you be better off to sell the T-bill on that day or hold it until maturity? Why?

Sale value after 4 weeks = Face Value / (1 + Interest * 9 weeks/52 weeks)

Sale value after 4 weeks = 100000 / (1 + 0.005192)

Sale value after 4 weeks = 99483.45

Annual Effective Interest Rate = Sale Value / Purchase price]^(52 / 4) - 1

Annual Effective Interest Rate = [99483.45 / 99255.58]^(52 / 4) - 1

Annual Effective Interest Rate = 1.002296^13 - 1

Annual Effective Interest Rate = 3.026%

Conclusion: It would be better if we hold the bond till maturity as annual effective rate if we hold till maturity (3.034%) is higher than the annual effective rate if we sell after 4 weeks

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