Question

Consider two bonds, a 3-year bond paying an annual coupon of 4%, and a 20-year bond, also with an annual coupon of 4%. Both bonds currently sell at par value. Now suppose that interest rates rise and the yield to maturity of the two bonds increases to 7%.a. What is the new price of the 3-year bond? (Round your answer to 2 decimal places.)b.What is the new price of the 20-year bond? (Round your answer to 2 decimal places.)

Answer 1

Answer:

a) $921.27

b) $682.18

Explanation:

Data provided in the question:

Annual coupon rate = 4%

Yield to maturity = 7%

Now,

Face value = $1,000

a) For 3-year bond

Price of Bond = $(C\times F\times(\frac{1-(1+R)^{-N}}{R}) + \frac{F}{(1+R)^N}$

here,

N is the number of periods

for 3 year bond, N = 3

Thus,

Price of Bond =$(0.04\times \ 1000\times(\frac{1-(1+0.07)^{-3}}{0.07}) + \frac{\ 1000}{(1+0.07)^3}$

= $104.97 + $816.30

= $921.27

b) For 20-year bond

Price of Bond = $(C\times F\times(\frac{1-(1+R)^{-N}}{R}) + \frac{F}{(1+R)^N}$

here,

N is the number of periods

for 20 year bond, N = 20

Thus,

Price of Bond = $(0.04\times \ 1000\times(\frac{1-(1+0.07)^{-20}}{0.07}) + \frac{\ 1000}{(1+0.07)^{20}}$

=  $423.76 + $258.42

= $682.18