Question

Suppose a​ ten-year, $1,000 bond with an 8.9% coupon rate and semiannual coupons is trading for $1,034.08.

a. What is the​ bond's yield to maturity​ (expressed as an APR with semiannual​ compounding)?

b. If the​ bond's yield to maturity changes to 9.2% ​APR, what will be the​ bond's price?

Answer 1

a

K = Nx2

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

k=1

K =10x2

1034.08 =∑ [(8.9*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^10x2

k=1

YTM% = 8.39

EAR = [(1 +stated rate/no. of compounding periods) ^no. of compounding periods - 1]* 100

0.0839 = ((1+Stated rate%/2*100)^2-1)*100

Stated rate% = 8.22

b

K = Nx2

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

k=1

K =10x2

Bond Price =∑ [(8.9*1000/200)/(1 + 9.2/200)^k]     +   1000/(1 + 9.2/200)^10x2

k=1

Bond Price = 980.66