Question

Suppose a​ ten-year, $ 1 comma $1,000 bond with an 8.5 % coupon rate and semiannual coupons is trading for $ 1 comma $1,035.59. 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 9.8 % ​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

1035.59 =∑ [(8.5*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^10x2

k=1

YTM% = 7.98

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

0.0798 = ((1+Stated rate%/2*100)^2-1)*100

Stated rate% = 7.83

b

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

Effective Annual Rate = ((1+9.8/2*100)^2-1)*100

Effective Annual Rate% = 10.04

K = Nx2

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

k=1

K =10x2

Bond Price =∑ [(8.5*1000/200)/(1 + 10.04/200)^k]     +   1000/(1 + 10.04/200)^10x2

k=1

Bond Price = 904.2