An investor purchased a 91-day, $100,000 T-bill on its issue date for $99,326.85. After holding it for 42 days, she sold the T-bill for a yield of 2.72%.
a)What was the original yield of the T-bill?
b)For what price was the T-bill sold?
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To calculate the original yield of the T-bill, we can use the formula:
Original yield = (Face value - Purchase price) / Purchase price * (360 / Number of days held)
a) Plugging in the provided values:
Face value = $100,000
Purchase price = $99,326.85
Number of days held = 42
Original yield = ($100,000 - $99,326.85) / $99,326.85 * (360 / 42)
Let's calculate this:
Original yield = ($673.15) / $99,326.85 * (360 / 42)
Original yield = 0.006776 * 8.57143
Original yield = 0.058
Therefore, the original yield of the T-bill was 5.8%.
b) To calculate the selling price of the T-bill, we can use the formula:
Selling price = Purchase price * (1 + Yield * Number of days held / 360)
Plugging in the provided values:
Purchase price = $99,326.85
Yield = 2.72%
Number of days held = 42
Selling price = $99,326.85 * (1 + 0.0272 * 42 / 360)
Let's calculate this:
Selling price = $99,326.85 * (1 + 0.000316)
Selling price = $99,326.85 * 1.000316
Selling price = $99,359.64
Therefore, the T-bill was sold for $99,359.64.
To find the answers to these questions, we need to understand the relationship between the purchase price, selling price, yield, and holding period.
Let's break down the information given:
- The investor purchased a 91-day T-bill for $99,326.85.
- The T-bill was held for 42 days.
- The T-bill was sold with a yield of 2.72%.
a) To find the original yield of the T-bill, we can use the formula for yield:
Yield = (Face Value - Purchase Price) / (Purchase Price) * (360 / Days Held)
In this case, the face value is $100,000, the purchase price is $99,326.85, and the number of days held is 42.
Plugging in the values, we get:
Yield = (100,000 - 99,326.85) / (99,326.85) * (360 / 42)
Calculating this expression, we find the original yield of the T-bill to be approximately 3.83%.
b) To find the selling price of the T-bill, we can use the formula:
Selling Price = Face Value / (1 + (Yield * Days Held) / 360)
In this case, the face value is $100,000, the yield is 2.72%, and the number of days held is 42.
Plugging in the values, we get:
Selling Price = 100,000 / (1 + (0.0272 * 42) / 360)
Calculating this expression, we find that the T-bill was sold for approximately $100,179.36.
So, to summarize:
a) The original yield of the T-bill was approximately 3.83%.
b) The T-bill was sold for approximately $100,179.36.