Question

Assume that a $1,000,000 par value, semiannual coupon US Treasury note with three years to maturity has a coupon rate of 6%. The yield to maturity (YTM) of the bond is 9.90%. Using this information and ignoring the other costs involved, calculate the value of the Treasury note:

Answer 1

The value of the Treasury note is $900865.5449 rounded off to $900865.55

Step-by-step explanation:

To calculate the price of the bond today, we will use the formula for the price of the bond. We assume that the interest rate provided is stated in annual terms. As the bond is a semi annual bond, the coupon payment, number of periods and semi annual interest rate in the market will be,

Coupon Payment (C) = 1,000,000 * 0.06 * 6/12 = $30000

Total periods (n) = 3 * 2 = 6

r or YTM = 0.099 * 6/12 = 0.0495 or 4.95%

The formula to calculate the price of the bonds today is attached.

Bond Price = 30000 * [( 1 - (1+0.0495)^-6) / 0.0495] +

1000000 / (1+0.0495)^6

Bond Price = $900865.5449 rounded off to $900865.55