Question

Assume that you wish to purchase a bond with a 30-year maturity, an annual coupon rate of 10 percent, a face value of $1,000, and semiannual interest payments. If you require a 9 percent nominal yield to maturity on this investment, what is the maximum price you should be willing to pay for the bond?

Answer 1

Answer:

present value of the bond discounted at 9% $1,103.19

Explanation:

We will calcualte the present value of the coupon payment and the maturity of the bonds a t the 9% market rate to know the present value of the bonds.

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

Cuopon payment: 1,000 x 10% /2 = $50 per payment

time 30 years x 2 payment per year = 60

rate 9% annual /2 = 4.5% semiannual = 0.045

$50 \times \frac{1-(1+0.045)^{-60} }{0.045} = PV$

PV $1,031.9011

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

Maturity   1,000.00

time        60

rate  0.045

$\frac{1000}{(1 + 0.045)^{60} } = PV$  

PV   71.2890

PV coupon payment $1,031.9011

PV maturity                       $71.2890

Total                          $1,103.1901