Question

A 20-year maturity bond with face value of $1,000 makes annual coupon payments and has a coupon rate of 8.8%. (Do not round intermediate calculations. Enter your answers as a percent rounded to 3 decimal places.)

a. What is the bond’s yield to maturity if the bond is selling for $980?

b. What is the bond’s yield to maturity if the bond is selling for $1,000?

c. What is the bond’s yield to maturity if the bond is selling for $1,180?

Answer 1

Given, the face value of the bond (F)= $1,000

Stated interest rate = 8.8% payable annually

Coupon amount (C) = $1,000 * 8.8% = $88

Maturity period (n) = 20 years

1. The bond is selling at (P) = $980

Yield to maturity = C+((F−P)/n)/(F+P)2 = $88+(($1000−$980)/20)/($1000+$980)/2 = 8.989%

2. The bond is selling at (P) = $1,000

Yield to maturity = C+((F−P)/n)/(F+P)2 = $88+(($1000−$1000)/20)/($1000+$1000)/2 = 8.800%

3. The bond is selling at (P) = $1,180

Yield to maturity = C+((F−P)/n)/(F+P)2 = $88+(($1000−$1180)/20)/($1000+$1180)/2 = 7.247%