Question

Assume that a $1,000,000 par value, semiannual coupon U.S. Treasury note with five years to maturity (YTM) has a coupon rate of 3%. The yield to maturity of the bond is 8.80%. Using this information and ignoring the other costs involved, calculate the value of the Treasury note:

Answer 1

$775,751

Step-by-step explanation:

the effective semiannual rate = 1.088 = (1 + r)²

r = 4.3072%

we must first determine the present value of the face value = $1,000,000 / (1 + 4.3072%)¹⁰ = $655,927.02

now the present value of the coupon payments = $15,000 x [1 - 1/(1 + i)ⁿ ] / i = $15,000 x [1 - 1/(1 + 0.043072)¹⁰ ] / 0.043072 = $119,823.98

market price = $775,751