Question

A U.S T-bill quote sheet has 150-day T-bills quoted at a discount rate of 4.93% (quoted for a 360-day year). If the bill has a $300000 face value, an investor could buy this bill for __________.

a.$298517.50
b.$285904.89
c.$285210.00
d.$314790.00
e.$293837.50
f.$300000.00
g.$293961.54

Answer 1

The investor could buy the 150-day T-bill quoted at a 4.93% discount rate with a $300,000 face value for approximately $293,842.50, with the closest answer choice being $293,837.50.

Step-by-step explanation:

To calculate the purchase price of a U.S Treasury bill (T-bill) quoted at a discount rate, we use the formula for discount yield. Given that we have a 150-day T-bill quoted at a 4.93% discount rate and a face value of $300,000, we can find the price at which an investor could buy the bill.

The formula to calculate the price (P) is as follows:

P = Face Value - (Face Value × (Discount Rate/360) × Days to Maturity)

Using the provided figures:

P = $300,000 - ($300,000 × (4.93/100/360) × 150)

P = $300,000 - ($300,000 × 0.0493 × (150/360))

P = $300,000 - ($300,000 × 0.0493 × 0.4167)

P = $300,000 - $6,157.50

P = $293,842.50

Looking at the given answer options, none exactly match the calculated value due to potential rounding differences. The closest option provided is $293,837.50, which might be the intended answer if we account for rounding in the original data or provided choices.