The price of a $100,000 182-days commercial paper sold 30 days after its issue date at a 5.35% yield is approximately $99,777.94, calculated by adjusting the yield for the remaining 152 days and discounting the face value to present value.
To calculate the price of a $100,000 182-days commercial paper sold 30 days after its issue date with a yield of 5.35%, we need to determine the remaining time for the commercial paper to mature and then discount the face value back to the present value using the yield.
First, we find the remaining maturity, which is 182 days - 30 days = 152 days. Next, we calculate the discount factor. The annual yield is 5.35%, but since we're dealing with a period less than a year, we need to adjust this yield to the proportion of the year the commercial paper will be held. The yield for 152 days is (5.35% / 365) * 152.
To find the present value, we use the formula: PV = FV / (1 + (r * t)), where PV is the present value, FV is the future value (face value), r is the yield rate (adjusted for the relevant time period), and t is the time remaining to maturity in years. Plugging the values in, we get:
PV = $100,000 / (1 + ((0.0535 / 365) * 152))
PV = $100,000 / (1 + 0.0022247)
PV = $100,000 / 1.0022247
PV = $99,777.94
Therefore, the price of the commercial paper is approximately $99,777.94.
Note that this is a simplified calculation and actual market calculations might take into account other factors such as actual/actual day counts, etc.