Final answer:
The purchase price for the T-bill is $966.67, calculated using the formula involving face value, discount rate, and days to maturity. The bond equivalent rate (AOR) when converting to a 365-day year is approximately 3.449%, calculated using the formula for Bond Equivalent Yield.
Step-by-step explanation:
To calculate the price you have to pay for a 60-day US Treasury bill (T-bill) with a face value of $1,000, quoted at a discount rate of 2%, you need to understand how T-bills are priced. The discount rate is applied to the face value to determine the amount by which the T-bill is discounted. The formula to find the purchase price is:
Purchase Price = Face Value - (Face Value × (Discount Rate × (Days to Maturity / 360)))
Using the given information: Purchase Price = $1,000 - ($1,000 × (0.02 × (60 / 360))) = $1,000 - ($1,000 × (0.02 × 1/6)) = $1,000 - $33.33 = $966.67. Hence, you have to pay $966.67 for this T-bill.
To find the Annualized Yield (AOR) on a 365-day year basis, you use the formula:
Bond Equivalent Yield (BEY) = (Face Value - Purchase Price) / Purchase Price × (365 / Days to Maturity)
Using the purchase price we calculated: BEY = ($1,000 - $966.67) / $966.67 × (365 / 60) = $33.33 / $966.67 × 6.083333 = .03449 or 3.449%.
The Annualized Yield or bond equivalent rate based on a 365-day year for this T-bill is therefore approximately 3.449%.