Final answer:
An investor could buy a 120-day T-bill with a 5.67 bid and a 5.61 ask rate and a $10,000 face value for $9,811.31. The purchase price is calculated based on the ask rate and the formula which accounts for the time to maturity.
Step-by-step explanation:
When considering the investment in Treasury bills (T-bills), particularly a 120-day T-bill with quotes of a 5.67 bid and a 5.61 ask and a $10,000 face value, we need to calculate the purchase price based on the ask rate. Investors would buy T-bills at the ask price rather than the bid price, which is the price at which sellers are willing to sell their securities.
The ask price is effectively the discounted yield that the investor will receive if they hold the T-bill until maturity. To calculate the actual purchase price of a T-bill with a specific face value and an ask rate, we can use the following formula:
Purchase Price = Face Value / (1 + (Ask Rate * (Days to Maturity/360)))
Applying this formula:
Purchase Price = $10,000 / (1 + (0.0561 * (120/360)))
Purchase Price = $10,000 / (1 + (0.0561 * 0.3333))
Purchase Price = $10,000 / 1.0187
Purchase Price = $9,811.31
Therefore, an investor could buy this 120-day T-bill for $9,811.31.