A T-bill with face value of $10,000 and 96 days to maturity is selling at a bank discount ask yield of 4.3%. A. What is the price of the bill? (use 360 days a year) B. what is its bond equivalent yield? A. .043 * (96/360) = .011 .011 * (1-.043) = $9,890 B. 1.1% * (365/96) = 4.182% Are these answers correct?
A. P = Po + Po*(r/360)*t = $10,000
Po + Po*(0.043/360)*96 = 10,000
Po + 0.01146667Po = 10000
1.01146667Po = 10000
Po = $9886.63. = Amt. paid.
B. %Yield=((10000-9886.63)/9886.63
*365/96 = 4.36
A. To calculate the price of the bill, you use the formula:
Price = Face Value / (1 + (Discount Rate * Days to Maturity / 360))
Using the given values:
Price = $10,000 / (1 + (0.043 * 96 / 360))
= $10,000 / (1 + (0.0116))
= $10,000 / 1.0116
= $9,886.23 (rounded to two decimal places)
Therefore, the correct price of the bill is $9,886.23.
B. To calculate the bond equivalent yield, you can use the formula:
Bond Equivalent Yield = (Discount Rate / (1 - Discount Rate)) * (365 / Days to Maturity)
Using the given values:
Bond Equivalent Yield = (0.043 / (1 - 0.043)) * (365 / 96)
= (0.043 / 0.957) * 3.802083
= 0.044862 * 3.802083
= 0.17085 (rounded to five decimal places)
= 17.085% (rounded to three decimal places)
Therefore, the correct bond equivalent yield is 17.085%.
Based on the calculations, the answers you provided are incorrect.
To determine if the answers provided are correct, let's go through the calculations step by step.
A. Price of the T-bill:
The bank discount yield is given as 4.3%, and the time to maturity is 96 days. We also need to use a 360-day year for this calculation.
First, we need to calculate the discount amount:
Discount = Face Value * Bank Discount Yield * (Days to Maturity / 360)
Substituting the given values:
Discount = $10,000 * 0.043 * (96/360)
Discount = $10,000 * 0.0113333
Discount ≈ $113.33
Now, we can calculate the price of the T-bill:
Price = Face Value - Discount
Price = $10,000 - $113.33
Price ≈ $9,886.67
So, the correct answer for the price of the T-bill is approximately $9,886.67 (rounded to the nearest cent).
B. Bond Equivalent Yield:
To convert the bank discount yield to bond equivalent yield, we need to account for the fact that the bank discount yield is calculated on a 360-day year, while the bond equivalent yield is based on a 365-day year.
The formula to convert bank discount yield to bond equivalent yield is as follows:
Bond Equivalent Yield = Bank Discount Yield * (365 / Days to Maturity)
Substituting the given values:
Bond Equivalent Yield = 0.043 * (365 / 96)
Bond Equivalent Yield ≈ 0.043 * 3.8020833
Bond Equivalent Yield ≈ 0.163519
To express the bond equivalent yield as a percentage, multiply by 100:
Bond Equivalent Yield ≈ 16.3519%
So, the correct answer for the bond equivalent yield is approximately 16.3519%.
Therefore, the correct answers are:
A. The price of the T-bill is approximately $9,886.67.
B. The bond equivalent yield is approximately 16.3519%.