Question

Suppose a​ ten-year, $ 1 comma 000 bond with an 8.7 % coupon rate and semiannual coupons is trading for $ 1 comma 035.86. 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 9.9 % ​APR, what will be the​ bond's price?

Answer 1

Given about a bond,

Years to maturity = 10 years

Face value = $1000

Coupon rate = 8.7% paid semiannually,

So, semiannual coupon payment = (8.7%/2) of 1000 = $43.50

Current price = $1035.86

Semiannual yield can be calculated on financial calculator using following values:

FV = 1000

PV = -1035.86

N = 2*10 = 20

PMT = 43.50

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

So, semiannual yield on the bond = 4.084%

Or annual yield = 2*4.084 = 8.17%

the​ bond's yield to maturity​ (expressed as an APR with semiannual​ compounding) is 8.17%

When YTM = 9.9%

Price of the bond can be calculated on financial calculator using following values:

FV = 1000

PMT = 43.5

N = 2*10 =20

I/Y = 9.9/2 = 4.95

compute for PV, we get PV = -924.91

So, bond's price = $924.91