Final answer:
The cost of a Treasury note is influenced by its face value, coupon rate, and the discount rate at which it is sold. A bond or note will cost less than its face value if the discount rate is higher than the bond's coupon rate. Without the exact discount rate, the precise cost of the Treasury note cannot be determined.
Step-by-step explanation:
The cost of a Treasury note is primarily determined by its face value and the interest rate, but to understand the actual cost, one would need to look at the discount rate at which the note will be sold. For instance, a simple two-year bond with a face value of $3,000 and a coupon rate of 8% will pay $240 (which is $3,000 × 8%) after the first year. After the second year, the bond pays another $240 in interest, along with the $3,000 principal amount. The present value of these future payments can be calculated using the present value formula, which discounts the future payments at a given discount rate.
If the discount rate is the same as the coupon rate (8%), the present value of the bond would equal its face value. However, if interest rates rise and the applicable discount rate becomes 11%, the present value of the bond would decrease as the future payments are discounted at a higher rate. As a result, one would expect to pay less than the face value for the bond when the discount rate exceeds the bond's coupon rate.
Applying this concept to the original question about the $5,000 13-week Treasury note, if the provided interest rate of 2.2% is the coupon rate, the cost would be calculated at a discount rate equal to the prevailing interest rate for a 13-week Treasury note. Without the actual discount rate or additional information (such as if it's a zero-coupon note), we cannot precisely calculate how much the note will cost you, but typically, it would cost slightly less than the face value if the note is sold at a discount.