Question

Suppose a ten-year, $1,000 bond with an 8.1% coupon rate and semi-annual coupons is trading for $1,034.69

A. What is the bond's yield to maturity(expressed an an APR with semi-annual compounding)?

B. If the bond's yield to maturity changes to 9.6% APR, what will be the bond's price?

Answer 1

Answer 2

Suppose a ten-year, $1,000 bond with an 8.1% coupon rate and semi-annual coupons is trading for $1,034.69

A. What is the bond's yield to maturity(expressed an an APR with semi-annual compounding)?

fv =1000 , pmt = 8.1%*1000*1/2 = 40.50 , pv = 1034.69, nper= 10*2 = 20

Rate = rate(nper,pmt,pv,fv)

Rate = rate(20,40.50,-1034.69,1000)

Rate = 3.80%

Bond's yield to maturity = 3.80*2 = 7.60%

B. If the bond's yield to maturity changes to 9.6% APR, what will be the bond's price?

fv =1000 , pmt = 8.1%*1000*1/2 = 40.50 , nper= 10*2 = 20, rate = 9.6/2 = 4.8%

Bond's price = pv(rate,nper,pmt,fv)

Bond's price = pv(4.8%,20,40.50,1000)

Bond's price = $ 904.93

Answer 3

Hi,

Part A:

Nper = 10*2 = 20 (indicates the period over which payments are made)

PMT = 1000*8.1%*1/2 = 40.5 (indicates the amount of semi-annual interest payment)

PV = -1034.69 (indicates the current trading price)

FV = 1000 (indicates the face value)

Rate = ? (indicates YTM)

Yield to Maturity = Rate(Nper,PMT,PV,FV)*2 = Rate(20,40.5,-1034.69,1000)*2 = 7.60%

Part B:

Nper = 10*2 = 20 (indicates the period over which payments are made)

PMT = 1000*8.1%*1/2 = 40.5 (indicates the amount of semi-annual interest payment)

Rate = 9.6%/2 (indicates YTM)

FV = 1000 (indicates the face value)

PV = ? (indicates the bond price)

Bond Price = PV(Rate,Nper,PMT,FV) = PV(9.6%/2,20,40.5,1000) = 904.93

Thanks.