QuestionJuly 16, 2025

A 3-month 28,000 treasury bill with a simple annual discount rate of 0.29% was sold in 2016.Assume 365 days in a year. (a) Find the price of the treasury bill (T-bill) (b) Find the actual interest rate paid by the Treasury (a) The price of the T-bill was 27979.70 (Round to the nearest cent as needed.) (b) The actual interest rate paid by the Treasury is square % (Type an integer or decimal rounded to five decimal places as needed.)

A 3-month 28,000 treasury bill with a simple annual discount rate of 0.29% was sold in 2016.Assume 365 days in a year. (a) Find the price of the treasury bill (T-bill) (b) Find the actual interest rate paid by the Treasury (a) The price of the T-bill was 27979.70 (Round to the nearest cent as needed.) (b) The actual interest rate paid by the Treasury is square % (Type an integer or decimal rounded to five decimal places as needed.)
A 3-month 28,000 treasury bill with a simple annual discount rate of 0.29% was sold in 2016.Assume 365 days in a year. (a) Find the price of the treasury bill (T-bill) (b) Find the actual interest rate paid by the Treasury (a) The price of the T-bill was 27979.70 (Round to the nearest cent as needed.) (b) The actual interest rate paid by the Treasury is square % (Type an integer or decimal rounded to five decimal places as needed.)

Solution
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Answer

0.00290% Explanation 1. Calculate the Discount Amount Use the formula for discount amount: D = \frac{r \times F \times t}{365}, where r = 0.0029, F = 28000, and t = 90 days. Calculate D = \frac{0.0029 \times 28000 \times 90}{365} = 20.30. 2. Calculate the Price of the T-bill Subtract the discount from the face value: P = F - D = 28000 - 20.30 = 27979.70. 3. Calculate the Actual Interest Rate Use the formula for actual interest rate: i = \frac{F - P}{P} \times \frac{365}{t}. Substitute F = 28000, P = 27979.70, and t = 90: i = \frac{28000 - 27979.70}{27979.70} \times \frac{365}{90} = 0.0029005.

Explanation

1. Calculate the Discount Amount<br /> Use the formula for discount amount: $D = \frac{r \times F \times t}{365}$, where $r = 0.0029$, $F = 28000$, and $t = 90$ days. Calculate $D = \frac{0.0029 \times 28000 \times 90}{365} = 20.30$.<br /><br />2. Calculate the Price of the T-bill<br /> Subtract the discount from the face value: $P = F - D = 28000 - 20.30 = 27979.70$.<br /><br />3. Calculate the Actual Interest Rate<br /> Use the formula for actual interest rate: $i = \frac{F - P}{P} \times \frac{365}{t}$. Substitute $F = 28000$, $P = 27979.70$, and $t = 90$: $i = \frac{28000 - 27979.70}{27979.70} \times \frac{365}{90} = 0.0029005$.
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