Question

Assuming semiannual compounding, what is the price of a zero coupon bond with 11 years to maturity paying $1,000 at maturity if the YTM is (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) 

а. 5 percent  _______ 

b. 9 percent _______ 

c. 13 percent _______ 

Answer 1

Number of periods to maturity = n = 11*2 = 22 semiannual periods

Par Value = FV = $1000

Yield to Maturity = r

Price of bond = PV = FV/(1+r)ⁿ

When YTM = 5%, Semiannual yield = r = 0.05/2 => PV = 1000/(1+0.05/2)²² = $580.86

When YTM = 9%, Semiannual yield = r = 0.09/2 => PV = 1000/(1+0.09/2)²² = $379.70

When YTM = 13%, Semiannual yield = r = 0.13/2 => PV = 1000/(1+0.13/2)²² = $250.21