A 30-year maturity bond with face value of $1,000 makes semiannual coupon paymen

Question

A 30-year maturity bond with face value of $1,000 makes semiannual coupon payments and has a coupon rate of 10%.

What is the bond’s yield to maturity if the bond is selling for $970? (Do not round intermediate calculations. Round your answer to 3 decimal places.)

What is the bond’s yield to maturity if the bond is selling for $1,170? (Do not round intermediate calculations. Round your answer to 3 decimal places.)

What is the bond’s yield to maturity if the bond is selling for $970? (Do not round intermediate calculations. Round your answer to 3 decimal places.)

Explanation / Answer

a.

Calculate Annual yield to maturity (YTM):

YTM = [C+(F-P)/n] / (F+P) / 2

C = Coupon / Interest payment = ($1,000 *10%)*6/12 = $50

F = Face value = $1,000

P = Price = $970

N = Years to maturity = 25 years

YTM = [$50 + ($1,000 - $970)/25] / ($1,000 + $970)/2

= 5.17%

Therefore, YTM is 5.17%.

b.

Calculate Annual yield to maturity (YTM):

YTM = [C+(F-P)/n] / (F+P) / 2

C = Coupon / Interest payment = ($1,000 *10%)*6/12 = $50

F = Face value = $1,000

P = Price = $1,000

N = Years to maturity = 25 years

YTM = [$50 + ($1,000 - $1,000)/25] / ($1,000 + $1,000)/2

= 5.00%

Therefore, YTM is 5.00%.

c.

Calculate Annual yield to maturity (YTM):

YTM = [C+(F-P)/n] / (F+P) / 2

C = Coupon / Interest payment = ($1,000 *10%)*6/12 = $50

F = Face value = $1,000

P = Price = $1,170

N = Years to maturity = 25 years

YTM = [$50 + ($1,000 - $1,170)/25] / ($1,000 + $1,170)/2

= 4.18%

Therefore, YTM is 4.18%.

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