Question

Suppose a​ ten-year, $1,000 bond with an 8.8% coupon rate and semiannual coupons is trading for $1,035.28.

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 9.4% APR, what will be the​ bond's price?

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

The​ bond's yield to maturity is blank%. (Round to two decimal​ places.)b. If the​ bond's yield to maturity changes to 9.4%​APR, what will be the​ bond's price?The new price for the bond is $blank. (Round to the nearest​ cent.)

Please show all work in steps with explanation. thanks.

Answer 1

a.

K = Nx2

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

k=1

K =10x2

1035.28 =∑ [(8.8*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^10x2

k=1

YTM% = 8.27

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

0.0827 = ((1+Stated rate%/2*100)^2-1)*100

Stated rate% = 8.11

b

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

Effective Annual Rate = ((1+9.4/2*100)^2-1)*100

Effective Annual Rate% = 9.62

K = Nx2

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

k=1

K =10x2

Bond Price =∑ [(8.8*1000/200)/(1 + 9.62/200)^k]     +   1000/(1 + 9.62/200)^10x2

k=1

Bond Price = 948.07