Final answer:
The current value of the U.S. Treasury note is calculated by discounting its semiannual interest payments and face value by its yield to maturity. The value of treasury note is $30,000 every six months.
Step-by-step explanation:
The value of a $1,000,000 par value, semiannual coupon U.S. Treasury note with two years to maturity and a coupon rate of 6% can be calculated by discounting its future cash flows by its yield to maturity (YTM) of 9.90%. The Treasury note will pay semiannual interest payments based on the coupon rate, which in this case is $1,000,000 * 6% / 2 = $30,000 every six months.
To find the present value (PV) of these payments, we need to discount each payment by the YTM using the formula for PV of an annuity. Additionally, the $1,000,000 face value due at maturity must be discounted back to the present value as well. By doing this, we will find the current market value of the Treasury note.
To clarify the effect of interest rates on the bond's price: When interest rates rise, bonds issued at lower interest rates will sell for less than face value, while bonds issued at higher rates will sell more than face value.
This is because investors demand a higher yield for taking on the risk of a bond with lower relative interest payments. Conversely, when interest rates fall, bonds with higher coupon rates become more attractive because they offer higher interest payments than newly issued bonds.