Final answer:
To find the bond equivalent yield of a Treasury bill, you calculate the profit made from the difference between the face value and the purchase price, adjust it for the 365-day year, and express it as a percentage. For a $100,000 T-bill with a 9% discount and 182-day maturity, the bond equivalent yield is 19.78%.
Step-by-step explanation:
The question is asking to calculate the bond equivalent yield of a Treasury bill that is selling at a discount. Given that the Treasury bill has a face value of $100,000 and is currently selling at 9% discount with a maturity of 182 days, we first need to determine the purchase price of the bill. Since the Treasury bill is sold at a discount, the investor will pay less than the face value. The discount can be calculated as 9% of the face value, which is $9,000. Therefore, the purchase price of the Treasury bill is $100,000 - $9,000 = $91,000.
Now, to calculate the yield, you need to consider the gain the investor will make, which is $100,000 - $91,000 = $9,000 over the period of 182 days. To annualize this yield and make it equivalent to a bond yield, we need to adjust this figure to a 365-day year. The bond equivalent yield formula is: ((Face value - Purchase price) / Purchase price) * (365 / Days to maturity).
In this case, the bond equivalent yield is ((100,000 - 91,000) / 91,000) * (365 / 182) = (9,000 / 91,000) * 2 = 0.0989 * 2 = 0.1978, or 19.78% when rounded to the nearest hundredth of a percent.