Suppose Hillard Manufacturing sold an issue of bonds with a 10-year maturity, a $1,000 par value, a 10% coupon rate, and semiannual interest payments.
a. Two years after the bonds were issued, the going rate of interest on bonds such as these fell to 6%. At what price would the bonds sell?
b. Suppose that 2 years after the initial offering, the going interest rate had risen to 12%. At what price would the bonds sell?
c. Suppose that 2 years after the issue date (as in part a) interest rates fell to 6%. Suppose further that the interest rate remained at 6% for the next 8 years. What would happen to the price of the bonds over time?

C) the price of the bonds will decrease over time. As the nominal amount will suffer from less discounting over time at maturity will match the nominal amount of $ 1,000. To do so It need to decrease over time.

Explanation:

The value of the bonds will be the present value of the future coupon payment and maturity at the new rate of 6%

PV of the coupon payment

[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]

C 50.000 (1,000 x 10% / 2 ayment per year)

time 16 (8 year to maturity x 2 payment per year)

rate 0.03 (6% over two payment per year)

[tex]50 \times \frac{1-(1+0.03)^{-16} }{0.03} = PV\\[/tex]

PV $628.0551

PV of the maturity

[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]

Maturity 1,000.00

time 16.00

rate 0.03

[tex]\frac{1000}{(1 + 0.03)^{16} } = PV[/tex]

PV 623.17

PV c $628.0551

PV m $623.1669

Total $1,251.2220

If the rate is 12%

PV of the coupon payment:

[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]

C 50.000

time 16

rate 0.06

[tex]50 \times \frac{1-(1+0.06)^{-16} }{0.06} = PV\\[/tex]

PV $505.2948

PV of the maturity:

[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]

Maturity 1,000.00

time 16.00

rate 0.06

[tex]\frac{1000}{(1 + 0.06)^{16} } = PV[/tex]

PV 393.65

PV c $505.2948

PV m $393.6463

Total $898.9410