Question

Roadside Markets has 8.45 percent coupon bonds outstanding that mature in 10.5 years. The bonds pay interest semiannually. What is the market price per bond if the face value is $1,000 and the yield to maturity is 7.2 percent?

Answer 1

Answer:

Total $1,091.0030

Explanation:

The market value of the bond will be the sum of the present value of the cuopon payment and the maturity date:

present alue of cuopon payment will be calculate as present value of an ordinary annuity:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 42.25   (1,000 face value x 8.45% /2 payment per year)

time 21 (10 years at 2 payment per year+ 1 payment)

rate 0.036   (here we use the YTM rate /2 because there are 2 payment per year)

$42.25 \times \frac{1-(1+0.036)^{-21} }{0.036} = PV$

PV $615.1803

Then, for the present value at maturity, we calculate the present value of a lump sum

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   1,000.00

time   21.00

rate  0.036

$\frac{1000}{(1 + 0.036)^{21} } = PV$  

PV   475.82

Finally, we add them both together

PV c $615.1803

PV m  $475.8227

Total $1,091.0030