Question

Suppose a 10 year bond with an 8/7% coupon rate and semi annual coupons is trading for $1035.91
a. What is the bonds yield to maturity ( expressed as an APR with semiannual compounding)?
b. If the bonds yield to maturity changes to 9/1% APR what will be the bonds price?

Answer 1

Given about a bond,

Years to maturity = 10

coupon rate = 8.7% paid semiannually

price = $1035.91

Face value = $1000

Semiannual coupon payment = (8.7%/2) of 1000 = $43.50

a). Yield to maturity on the bond can be calculated on financial calculator using following values:

FV = 1000

PMT = 43.50

PV = -1035.91

N = 2*10 = 20

Compute for I/Y, we get I/Y = 4.084

So, semi annual YTM = 4.084%

Hence Yield to maturity of the bond = 2*4.084% = 8.17%

b). If YTM changes to 9.1%, Price of the bond can be calculated on financial calculator using following values:

FV = 1000

PMT = 43.50

N = 2*10 = 20

I/Y = 9.1/2 = 4.55

compute for PV, we get PV = -974.10

=> Price of the bond will be $974.10