Question

Consider three bonds with 6.1% coupon rates, all selling at face value. The short-term bond has a maturity of 4 years, the intermediate-term bond has maturity 8 years, and the long-term bond has maturity 30 years.

a. What will be the price of each bond if their yields increase to 7.1%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

4 Years :

8 Years:

30 Years:

b. What will be the price of each bond if their yields decrease to 5.1%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

4 Years:

8 Years :

30 Years :

Please show work!

Answer 1

	The price of a bond is the PV of the expected
	cash flows from the bond discounted at the
	market rate of interest.
	The expected cash flows in the case are:
	*The maturity value of $1000, and
	*The annual interest of $61, which is an annuity.
	The calculations are made below:
a]	Maturity of 4 Years = 1000/1.071^4+61*(1.071^4-1)/(0.071*1.071^4) =	$     966.20
	Maturity of 8 Years = 1000/1.071^8+61*(1.071^8-1)/(0.071*1.071^8) =	$     940.52
	Maturity of 30 Years = 1000/1.071^30+61*(1.071^30-1)/(0.071*1.071^30) =	$     877.15
b]	Maturity of 4 Years = 1000/1.051^4+61*(1.051^4-1)/(0.051*1.051^4) =	$ 1,035.38
	Maturity of 8 Years = 1000/1.051^8+61*(1.051^8-1)/(0.051*1.051^8) =	$ 1,064.37
	Maturity of 30 Years = 1000/1.051^30+61*(1.051^30-1)/(0.051*1.051^30) =	$ 1,151.99