Question

Fill in the table below for the following zero-coupon bonds, all of which have par values of $1,000. Use semi-annual periods.

Price Maturity (Years) Yield to Maturity

390 20 ?

610 20 ?

490 10 ?

? 10 9.90  

?    10 6.90

390 ? 7.90

Answer 1

1)

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =20x2

390 =∑ [(0*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^20x2

k=1

YTM% = 4.76

2)

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =20x2

610 =∑ [(0*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^20x2

k=1

YTM% = 2.49

3)

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =10x2

490 =∑ [(0*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^10x2

k=1

YTM% = 7.26

4)

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =10x2

Bond Price =∑ [(0*1000/200)/(1 + 9.9/200)^k]     +   1000/(1 + 9.9/200)^10x2

k=1

Bond Price = 380.5

5)

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =10x2

Bond Price =∑ [(0*1000/200)/(1 + 6.9/200)^k]     +   1000/(1 + 6.9/200)^10x2

k=1

Bond Price = 507.45

6)

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =Nx2

390 =∑ [(0*1000/200)/(1 + 7.9/200)^k]     +   1000/(1 + 7.9/200)^Nx2

k=1

N(in years) = 12.15